Math calculators
Geometry, algebra, arithmetic and trigonometry, solved step by step.
383 published calculatorsArithmetic 75
Absolute Change Calculator Calculate absolute change, relative change, and percentage change between two values. See step-by-step working, a comparison visual, and plain-English interpretation.
Open Absolute Value Calculator Find |x|, solve absolute value equations like |ax+b|=c, solve inequalities, and find the distance between two points. Full step-by-step work shown.
Open Adding and Subtracting Fractions Calculator Add or subtract fractions and mixed numbers instantly. Shows every step: find the LCD, convert, combine, and simplify. Handles unlike denominators automatically.
Open Addition Calculator Add up to 6 numbers at once and see a step-by-step column-by-column breakdown. Supports decimals, negatives, and shows count, average, min, max, and range.
Open Associative Property Calculator Verify the associative property instantly for addition or multiplication. Enter three numbers, see both groupings computed step by step, and confirm they are equal.
Open Average Calculator: Mean, Median, Mode, Std Dev Calculate arithmetic mean, geometric mean, harmonic mean, median, mode, range, and standard deviation for any list of numbers in one step.
Open Ceiling Function Calculator Calculate the ceiling (round-up) of any real number instantly. See step-by-step working, floor comparison, fractional part, and a visual number-line chart.
Open Chinese Remainder Theorem Calculator Solve any system of simultaneous modular congruences with the Chinese Remainder Theorem. Get the smallest solution, the period, and a full step-by-step proof.
Open Compatible Numbers Calculator Round any two numbers to compatible values and instantly estimate their sum, difference, product, or quotient. Shows rounding steps and percentage error.
Open Consecutive Integers Calculator Find consecutive integers whose sum or product equals a target, list any sequence, and switch between any, even, or odd consecutive integers. Step-by-step workings.
Open Cross Multiplication Calculator Solve any proportion A/B = C/D for the missing value instantly. Enter three numbers and get the fourth with full step-by-step working shown.
Open Cube Root Calculator Find the cube root of any real number, compute any nth root, or reverse-solve to find a number from its root. Includes steps, chart, and a perfect-cube table.
Open Decimal Calculator: Add, Subtract, Multiply, Divide and More Add, subtract, multiply, divide, raise to a power, take an nth root, or find the logarithm of two decimals. See step-by-step working and choose rounding precision.
Open Digit Sum Calculator Calculate the digit sum and digital root of any integer instantly. Shows step-by-step addition, divisibility by 3 and 9, Harshad number check, and worked examples.
Open Digital Root Calculator Calculate the digital root of any integer instantly. See every digit-sum step, use the closed-form formula, explore bases 2-36, and learn the math behind it.
Open Distributive Property Calculator Instantly apply the distributive property to numeric or algebraic expressions. See a(b + c) = ab + ac worked out step by step with every calculation shown.
Open Divisibility Test Calculator Check if any integer is divisible by 2 through 13 instantly. See the divisibility rule applied step by step for each divisor, with quotient and remainder.
Open Egyptian Fractions Calculator Convert any fraction into a sum of distinct unit fractions (Egyptian fractions). Choose your algorithm, see step-by-step work, and explore this 3,700-year-old notation.
Open Expanded Form Calculator Convert any number to expanded form instantly. See expanded notation, factor form, exponential form and word form side by side with a place-value breakdown.
Open Factor Calculator Find every factor, factor pair, prime factorization, and factor sum for any positive integer. Detects prime, perfect square, and perfect cube numbers instantly.
Open Factorial Calculator Calculate standard, double, subfactorial, multifactorial, and primorial. Get exact value, scientific notation, digit count, and trailing zeros instantly.
Open Fermat's Little Theorem Calculator Apply Fermat's Little Theorem instantly: enter a and p to compute a^(p-1) mod p, verify the result is 1, find the modular inverse, and see the full step-by-step proof.
Open Floor Function Calculator Calculate the floor, ceiling, round, truncate and fractional part of any real number instantly. See the step-by-step breakdown and key properties of the floor function.
Open Fundamental Counting Principle Calculator Multiply independent events to count total outcomes instantly. Enter up to 6 event choices, see step-by-step working, and track how the product grows with each event.
Open GCF and LCM Calculator Calculate GCF and LCM for up to 6 numbers. See step-by-step prime factorization, divisors list, and the GCF x LCM relationship formula with a worked example.
Open Geometric Mean Calculator Calculate the geometric mean of any positive numbers or growth rates. Compare arithmetic and harmonic means, reverse-solve for CAGR, and see a compounding schedule.
Open Greater Than or Less Than Calculator Compare any two numbers instantly: integers, decimals, negatives, and fractions. See the symbol (>, <, =), the difference, the ratio, and step-by-step reasoning.
Open Harmonic Mean Calculator Calculate harmonic mean with optional weights. Compare it instantly against arithmetic and geometric means. Shows every step, use cases for speed, P/E ratios, and more.
Open Integer Calculator Add, subtract, multiply, or divide any two integers instantly. See the sign rules, step-by-step working, quotient and remainder, and binary/octal/hex conversions.
Open Inverse Modulo Calculator Find the modular multiplicative and additive inverse instantly. Shows Extended Euclidean Algorithm steps, existence conditions, and a worked example.
Open LCM Calculator - Least Common Multiple Find the least common multiple of up to 6 numbers instantly. See the prime factorization, step-by-step working, GCD method, and divisibility rules.
Open Long Addition Calculator Add multiple numbers instantly and see each column worked out with carries, exactly as on paper. Whole numbers and decimals supported. Free.
Open Long Division Calculator Divide any two numbers (including decimals and negatives) to get the quotient, remainder, simplified fraction, mixed number, and decimal result with step-by-step work.
Open Long Multiplication Calculator Multiply any two numbers with full step-by-step long multiplication shown. Supports integers, decimals, and negatives. See every partial product clearly.
Open Long Subtraction Calculator Subtract any two whole or decimal numbers using the column method. Shows every regrouping (borrowing) step, place-by-place, with the full worked solution.
Open Magic Square Calculator Generate magic squares from 3x3 to 9x9 instantly. Calculates the magic constant, sum of all numbers, number count, and construction method with step-by-step working.
Open Mean Calculator Calculate the arithmetic, geometric, harmonic, or weighted mean of any data set. Also get median, mode, range, variance, and standard deviation instantly.
Open Modulo Calculator Calculate a mod n with full modular arithmetic: remainder, quotient, power mod, modular addition, subtraction, multiplication, and a congruence check.
Open Multiplication Calculator Multiply up to 10 numbers at once, see long-multiplication steps digit by digit, or solve for a missing factor. Covers decimals, negatives, and sign rules.
Open Multiplicative Inverse Calculator Find the multiplicative inverse (reciprocal) of any integer, decimal, fraction, or mixed number instantly. Includes step-by-step working and a modular inverse mode.
Open Multiplicative Inverse Modulo Calculator Find the multiplicative or additive modular inverse instantly. Shows full Extended Euclidean Algorithm steps, GCD check, and Fermat shortcut for prime moduli.
Open Order of Magnitude Calculator Find the order of magnitude of any number, convert to scientific notation, and compare two values by how many powers of 10 separate them. Instant, free results.
Open Partial Products Calculator Break any multiplication into place-value partial products instantly. See every step, a full grid breakdown, and the final answer with clear working shown.
Open Perfect Cube Calculator Find any number cubed (n^3), check if a number is a perfect cube, and calculate cube roots instantly. Includes a reference table of the first 50 perfect cubes.
Open Perfect Square Calculator Check whether any number is a perfect square, find its root, reverse-calculate n squared from a root, or list every perfect square inside a range. Step-by-step shown.
Open Pi Experiments Calculator Estimate pi from five classic experiments: circumference ratio, Archimedes slices, Buffon's needle, pendulum timing, and Monte Carlo dart-throw. Full step-by-step math.
Open Place Value Calculator Find the place value of every digit in any number. See expanded form, word form, and a digit-by-digit table from ones through quintillions and tenths to billionths.
Open Polish Notation Converter Convert any math expression between infix, prefix (Polish), and postfix (RPN) notation. Evaluate numeric expressions step by step. Free, instant, no install.
Open Power Mod Calculator Compute a^b mod n instantly with the binary square-and-multiply algorithm. See the full step-by-step table, binary exponent breakdown, and key properties.
Open Powers of i Calculator Calculate any power of the imaginary unit i. Enter an integer exponent for the exact result, step-by-step working, real and imaginary parts, and the cycle table.
Open Prime Factorization Calculator Find the prime factorization, all divisors, divisor count, sum of divisors, and Euler totient of any integer. Factor trees, exponent form, and CSV output included.
Open Prime Number Calculator Check if any whole number is prime, get its full prime factorization, all divisors, and the nearest prime numbers above and below it.
Open Quotient Calculator Find the quotient, remainder, decimal result, and mixed-number form instantly. Shows step-by-step division work and handles negative numbers.
Open Radical Calculator Simplify any radical expression step by step. Enter a coefficient, root index, and radicand to get the simplified form, prime factorization, and decimal value instantly.
Open Rationalize Denominator Calculator Rationalize a denominator instantly. Handles monomial square roots, binomial conjugates, cube roots, and nth roots. Full step-by-step working shown.
Open Reciprocal Calculator Find the reciprocal of any decimal, fraction, or mixed number. Get 1/x as a decimal, simplified fraction, and scientific notation with full step-by-step working.
Open Relatively Prime Calculator Check instantly if two integers are relatively prime (coprime). See the GCD via the Euclidean algorithm, prime factorizations, LCM, and step-by-step working.
Open Remainder Calculator Find the remainder and quotient of any division instantly. Supports truncated, floored, and Euclidean modulo conventions plus fraction and R-notation output.
Open Reverse FOIL Calculator Factor any quadratic trinomial ax^2 + bx + c into two binomials using the reverse FOIL (AC) method. Instant step-by-step solution with worked math.
Open Root Calculator Calculate any root: square root, cube root, or nth root instantly. Step-by-step estimation, perfect root detection, negative support, and a root curve chart.
Open Root Mean Square Calculator Calculate the root mean square (RMS) of any dataset instantly. See the step-by-step working, arithmetic mean, standard deviation, and AC voltage conversion.
Open Round to the Nearest Thousand Calculator Round any number to the nearest thousand, ten thousand, or hundred thousand instantly. Supports 7 rounding modes with step-by-step explanations.
Open Rounding Numbers Calculator Round any number to decimal places, significant figures, or a whole-number place value. Choose from 9 rounding modes with a full step-by-step explanation.
Open Scientific Notation Calculator Convert numbers to/from scientific notation and do arithmetic in scientific notation. Get E-notation, engineering notation with SI prefix, and step-by-step working.
Open Set Builder Calculator Free set calculator for union, intersection, difference, complement, power set, and Cartesian product. Enter finite sets and get instant results with step-by-step work.
Open Significant Figures Calculator Count significant figures in any number, round to a chosen precision, or add, subtract, multiply, and divide with correct sig fig rules and step-by-step results.
Open Simplifying Radicals Calculator Simplify any radical instantly: enter the index, radicand and outer coefficient, get the simplified form with step-by-step prime factorization and a decimal value.
Open Square Root Calculator Find the square root, cube root, or any nth root of a number. Simplify radicals, reverse-solve, spot perfect squares, and see step-by-step working.
Open Standard Form Calculator Convert any number to standard form (scientific notation), E-notation, or engineering notation instantly. See step-by-step working and switch between all four formats.
Open Subtracting Fractions Calculator Subtract any two fractions or mixed numbers instantly. See the LCD, step-by-step working, simplified result, and decimal equivalent in one click.
Open Subtraction Calculator Subtract up to four numbers instantly. Shows a step-by-step breakdown, handles decimals and negatives, and explains regrouping (borrowing) in plain language.
Open Sum of Products Calculator Calculate the sum of products of two numeric series instantly. See every multiplication step, the running total, weighted average, and the full worked solution.
Open Terminating Decimals Calculator Check whether a fraction gives a terminating or repeating decimal. See the prime factorisation, simplified fraction, decimal expansion, and step-by-step working.
Open Triangular Numbers Calculator Calculate any triangular number instantly with T(n) = n(n+1)/2. Reverse-solve to find position n, display a sequence up to 20 terms, and see step-by-step working.
Open Weighted Average Calculator Calculate a weighted average for grades, GPA, or portfolios. Get the weighted mean, simple mean, per-item breakdown, and a reverse-solve for a target score.
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Average Rate of Change Calculator Calculate the average rate of change between two points or over a function interval. See the formula, step-by-step working, secant line, and real-world interpretation.
Open Bilinear Interpolation Calculator Estimate a value at any point inside a 2D grid cell from four known corner values. See the full step-by-step working, the formula, and intermediate results instantly.
Open Catenary Curve Calculator Calculate the catenary curve shape parameter, sag, arc length, cable tension, and support angle. Switch between metric and imperial units with a live curve chart.
Open Coordinate Grid Calculator Calculate distance, midpoint, slope, line equation, angle of inclination, and perpendicular bisector between two points on the coordinate grid instantly.
Open Cosine Similarity Calculator Calculate cosine similarity, cosine distance, and the angle between two vectors in 2 to 6 dimensions. Step-by-step dot product and magnitude breakdown included.
Open Cross Product Calculator Find the cross product a x b, unit normal vector, angle between vectors, parallelogram area, triangle area, and scalar triple product. Full step-by-step working shown.
Open Direction of the Vector Calculator Find the direction angle, direction cosines, magnitude, and unit vector for any 2D or 3D vector. Shows quadrant-aware angle in degrees and radians with step-by-step work.
Open Distance Calculator Calculate the distance between two points in 2D or 3D using the Euclidean distance formula. See the step-by-step working, midpoint, slope and a live diagram.
Open Distance from Point to Plane Calculator Calculate the perpendicular distance from any 3D point to a plane instantly. Enter plane coefficients or a normal vector, see the formula and step-by-step working.
Open Dot Product Calculator Compute the dot product, angle, scalar and vector projections for 2D or 3D vectors. Also solve from magnitudes and angle. Step-by-step work shown.
Open Endpoint Calculator Find the missing endpoint of a line segment from one endpoint and the midpoint. Supports 2D and 3D, shows step-by-step working, distance, and a coordinate graph.
Open Equation of a Sphere Calculator Find the standard and general equation of a sphere from center and radius, diameter endpoints, or expanded coefficients. Get volume, surface area, and step-by-step derivation.
Open Gradient Calculator Calculate the gradient (slope) between two points or from rise and run. Get the angle in degrees, percent grade, distance, and a full step-by-step worked solution.
Open Intersection of Two Lines Calculator Find where two lines cross. Supports slope-intercept and standard form. Shows step-by-step algebra, the intersection formula, and handles parallel or coincident lines.
Open Irregular Polygon Area Calculator Calculate the area, perimeter, and centroid of any irregular polygon from vertex coordinates. Uses the Shoelace formula with a full step-by-step breakdown.
Open Latus Rectum Calculator Calculate the latus rectum length and endpoint coordinates for any conic section - parabola, ellipse, or hyperbola - with step-by-step working and formulas.
Open Least Squares Regression Line Calculator Find the least squares regression line (LSRL) instantly: enter x and y data pairs to get the slope, y-intercept, R-squared, correlation, and a step-by-step solution.
Open Line Equation from Two Points Calculator Enter two points and get the line equation in slope-intercept, standard, point-slope, and parametric forms, plus slope, intercepts, angle, distance, and midpoint.
Open Line of Intersection of Two Planes Calculator Find where two planes meet. Enter plane coefficients (ax+by+cz=d) and get the direction vector, a point on the line, parametric equations, and the angle between planes.
Open Linear Interpolation Calculator Instantly interpolate (or extrapolate) a y-value for any x between two known data points. Shows the slope, y-intercept, equation, worked steps, and a live chart.
Open Manhattan Distance Calculator Calculate Manhattan distance (L1 norm) in 2D, 3D or 4D. Step-by-step breakdown, Euclidean comparison, real-world use cases for grids, ML, and robotics.
Open Midpoint Calculator Find the midpoint of two points in 2D or 3D, or reverse-solve for a missing endpoint. Also shows the distance between the endpoints and fraction results.
Open Parabola Calculator Calculate vertex, focus, directrix, axis of symmetry, latus rectum and intercepts for any parabola from standard or vertex form. Step-by-step workings shown.
Open Parallel Line Calculator Find the equation of a line parallel to any given line through a specific point. Get the y-intercept, distance between lines, and a step-by-step solution instantly.
Open Perpendicular Line Calculator Find the equation of a perpendicular line through any point. Enter slope-intercept, two-point, or standard form. Shows slope, equation, intersection point, and steps.
Open Point-Slope Form Calculator Convert a slope and point (or two points) into point-slope, slope-intercept, and standard form. Includes x-intercept, angle, and parallel/perpendicular slopes.
Open Polar Coordinates Calculator Convert rectangular (x, y) to polar (r, theta) or polar to rectangular instantly. Choose degrees or radians. See the worked steps and a coordinate diagram.
Open Polynomial Graphing Calculator Graph any polynomial up to degree 5. Instantly find real roots, local maxima and minima, inflection points, increasing/decreasing intervals, and end behavior.
Open Ratios of Directed Line Segments Calculator Find the point dividing a directed segment AB in ratio m:n (internal or external), or reverse-solve the ratio from three collinear points. Steps shown.
Open Rise Over Run Calculator Calculate slope from two points using rise over run. Get the slope as a fraction, decimal, percent grade, angle in degrees, and 2D distance instantly.
Open Rotation Calculator Rotate any point or coordinate pair around the origin or a custom center. Supports degrees and radians, clockwise or counterclockwise, with step-by-step working.
Open Scatter Plot Calculator Enter up to 10 (x, y) data pairs to get the linear regression equation, slope, intercept, Pearson r, R-squared, RMSE, and descriptive statistics instantly.
Open Slope Calculator Find slope, angle, distance, percentage grade, y-intercept, x-intercept, and the full line equation from two points or one point plus slope.
Open Slope-Intercept Form Calculator Find y = mx + b from two points, a point and slope, or slope and y-intercept. Outputs include x-intercept, angle, standard form, and a table of values.
Open Spherical Coordinates Calculator Convert between Cartesian, spherical, and cylindrical coordinates instantly. Supports degrees and radians with full step-by-step working and formulas.
Open Standard Form to Slope-Intercept Form Calculator Convert Ax + By + C = 0 to y = mx + b instantly. Get slope, y-intercept, x-intercept, angle, and step-by-step working with a live graph.
Open Three-Dimensional Distance Calculator Calculate the straight-line distance between two points in 3D space. Get the midpoint, direction vector, unit vector, and axis deltas instantly.
Open Triangulation Calculator Find an unknown point using triangulation (two bearings) or trilateration (two distances). Shows coordinates, azimuth, step-by-step working, and a live diagram.
Open Unit Vector Calculator Find the unit vector (normalized vector) for any 2D or 3D vector. Shows magnitude, unit components, direction angles, and step-by-step working.
Open Vector Addition Calculator Add or subtract two vectors in 2D or 3D, enter components or magnitude and angle, get the resultant vector, its magnitude, direction angle, and full worked steps.
Open Vector Calculator Vector calculator for 2D and 3D: magnitude, addition, subtraction, dot product, cross product, unit vector, and angle between vectors - with full step-by-step working.
Open Vector Magnitude Calculator Compute the magnitude of a 2D, 3D, 4D or 5D vector. Get unit-vector components, direction angles and cosines, plus a full step-by-step working.
Open Vector Projection Calculator Calculate the vector projection, scalar projection, orthogonal component, dot product, and angle between two vectors in 2D or 3D. Full step-by-step working shown.
Open Vertex Form Calculator Convert ax²+bx+c to vertex form a(x-h)²+k, or go the other way. Finds vertex, roots, y-intercept, axis of symmetry, focus, and discriminant with full steps.
Open Volume of a Parallelepiped Calculator Calculate the volume and surface area of a parallelepiped using three vectors, edge lengths and angles, or four vertices. Includes step-by-step working.
Open Y-Intercept Calculator Find the y-intercept, x-intercept, slope and full equation from a slope and point, two points, or standard form ax + by + c = 0. Step-by-step solution shown.
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Absolute Value Equation Calculator Solve absolute value equations of the form |ax+b|+c=d step by step. Find both solutions, see the split into positive and negative cases, and visualize the number line.
Open Absolute Value Inequalities Calculator Solve any absolute value inequality of the form a|bx + c| + d < e instantly. Get the solution set, interval notation, AND/OR logic, and a worked step-by-step breakdown.
Open Adding and Subtracting Polynomials Calculator Add or subtract two polynomials up to degree 6, with full step-by-step working, like-terms grouping, and the simplified result. Free and instant.
Open Bessel Function Calculator: J, Y, I and K Functions Calculate Bessel functions J_n(x), Y_n(x), I_n(x) and K_n(x) for any integer order 0-5 and real argument. Includes the math steps, a value chart, and a reference table.
Open Binomial Coefficient Calculator (nCr) Calculate C(n,k) instantly. Get nCr, nPr, combinations with repetition, step-by-step factorial work, Pascal's triangle row, and a bar chart - all free.
Open Box Method Calculator Multiply any two whole numbers using the box (area) method. See every partial product in the grid, follow the step-by-step breakdown, and check your work instantly.
Open Completing the Square Calculator Convert ax2 + bx + c to vertex form and find real or complex roots by completing the square. Shows every step, discriminant, and the parabola chart.
Open Complex Conjugate Calculator Find the complex conjugate of any complex number instantly. Get z-bar, modulus |z|, modulus squared |z|^2, argument, polar form, and step-by-step working shown.
Open Complex Number Calculator Perform arithmetic on complex numbers in a+bi form. Get results in rectangular, polar, exponential, and trig (CIS) form, with every step shown.
Open Complex Root Calculator Find all n distinct nth roots of any complex number in Cartesian, polar, and exponential form. Uses De Moivre's theorem with step-by-step working.
Open Cubic Equation Calculator Solve any cubic equation ax3 + bx2 + cx + d = 0. Get all three roots (real and complex), the discriminant, Vieta sums, and a full show-your-work breakdown.
Open Descartes' Rule of Signs Calculator Count the possible positive and negative real roots of any polynomial up to degree 6 using Descartes' Rule of Signs. See every valid root combination instantly.
Open Diamond Problem Calculator Solve any diamond math problem instantly. Enter two known values (product, sum, or side numbers) and get all four answers with full step-by-step working.
Open Direct Variation Calculator Solve direct variation (y = kx) for any unknown: find y, x, or the constant k. Includes two-point mode, proportion solver, steps, and a real-world examples table.
Open Discriminant Calculator Find the discriminant of any quadratic, cubic or quartic polynomial. See the root count, root values, vertex, axis of symmetry and full step-by-step work.
Open Elimination Method Calculator Solve 2x2 or 3x3 systems of linear equations by elimination with full step-by-step working, special-case detection, and instant results.
Open Error Function Calculator Calculate erf(x), erfc(x), and erfcx(x) online. Inverse erf and erfc included. Step-by-step panel, curve visual, and reference table from x = 0 to 3.
Open Factoring Trinomials Calculator Factor any trinomial ax2 + bx + c instantly. See the AC method, perfect square, and difference of squares steps shown with your numbers.
Open FOIL Calculator Multiply two binomials with the FOIL method instantly. Enter a, b, c, d for (ax+b)(cx+d) and get every step: First, Outer, Inner, Last, and the simplified result.
Open Gamma Function Calculator Calculate the Gamma function Gamma(x) for any real number. Get the result, ln|Gamma(x)|, factorial equivalent, and a step-by-step worked solution instantly.
Open Graphing Inequalities on a Number Line Calculator Graph linear inequalities on a number line instantly. Get interval notation, set-builder notation, direction arrows, open/closed circles, and step-by-step solutions.
Open Graphing Quadratic Inequalities Calculator Solve any quadratic inequality ax^2 + bx + c vs d. Get the solution in interval notation, discriminant, vertex, roots, and a full step-by-step worked solution.
Open Hyperbolic Functions Calculator Calculate all 6 hyperbolic functions (sinh, cosh, tanh, coth, sech, csch) and all 6 inverse hyperbolic functions instantly. See the worked steps and formulas.
Open Inequality to Interval Notation Calculator Convert any inequality to interval notation instantly. Supports one-sided, two-sided and compound OR inequalities, with set-builder notation and steps.
Open Interval Notation Calculator Convert inequalities to interval notation and back. Get interval length, set-builder form, midpoint, and step-by-step work for open, closed, or half-open intervals.
Open Inverse Variation Calculator Solve for x, y, or k in the inverse variation equation y = k/x. Enter any two known values and get the third, with full steps and a live curve chart.
Open Multiplying Binomials Calculator Multiply two binomials instantly using the FOIL method. Get the expanded trinomial, all four FOIL steps shown, and the product pattern identified.
Open Multiplying Polynomials Calculator Multiply two polynomials of any degree up to 6 instantly. Shows the full distributive-property expansion and simplified result with every term labeled.
Open Partial Fraction Decomposition Calculator Decompose a rational function into partial fractions instantly. Choose your denominator form, enter coefficients, and get constants A, B, C with step-by-step workings.
Open Perfect Square Trinomial Calculator Check if ax² + bx + c is a perfect square trinomial, get the factored binomial form, or find a missing term. Includes step-by-step working and examples.
Open Polynomial Division Calculator Divide any polynomial by another with full long-division steps, quotient, remainder, and the factor theorem check. Works with degrees 0 through 5.
Open Power Set Calculator Enter any set of elements and instantly get its power set: total subset count, proper subset count, k-element subset counts, and a full enumerated list.
Open Quadratic Formula Calculator Solve ax+bx+c=0 instantly. Get both roots, the discriminant, vertex, axis of symmetry, factored form, vertex form, and step-by-step work.
Open Quaternion Calculator Free quaternion calculator: add, subtract, multiply, divide, find the norm, conjugate, inverse, and generate rotation quaternions from axis and angle.
Open Rational Zeros Calculator Find all possible rational zeros of any polynomial up to degree 8. Enter coefficients to get every p/q candidate, actual rational roots, and synthetic division steps.
Open Rectangle Calculator Calculate the area, perimeter, diagonal, circumradius, and inradius of a rectangle in metric or imperial units. Solve from any two known values instantly.
Open Subset Calculator Find all subsets (power set) of any set in seconds. Enter your elements to count total subsets, proper subsets, and see every subset listed with step-by-step working.
Open Substitution Method Calculator Solve a system of two linear equations by substitution. See every algebraic step: isolate a variable, substitute, simplify, and back-solve. Instant results.
Open Synthetic Division Calculator Divide any polynomial by a linear factor using synthetic division. Get the quotient polynomial, remainder, full equation, and step-by-step tableau instantly.
Open System of Equations Calculator Solve 2x2 or 3x3 linear systems instantly. Choose Cramer's rule or Gaussian elimination, get exact fractions, and see every step shown clearly.
Open Union and Intersection Calculator Find the union, intersection, difference, and symmetric difference of two sets. Get cardinalities, the inclusion-exclusion formula, and a full step-by-step solution.
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Adjoint Matrix Calculator Calculate the adjoint (adjugate) of a 2x2, 3x3, or 4x4 matrix instantly. Shows cofactor matrix, determinant, inverse, and every step of the working.
Open Characteristic Polynomial Calculator Find the characteristic polynomial p(lambda) = det(A - lambdaI) for 2x2, 3x3 or 4x4 matrices. Get eigenvalues, trace, determinant, and full step-by-step working.
Open Cholesky Decomposition Calculator Compute the Cholesky factorization A = LL^T for 2x2 and 3x3 symmetric positive-definite matrices. See every step, the LDL decomposition, and the verification check.
Open Cofactor Expansion Calculator Calculate the determinant of any 2x2, 3x3, or 4x4 matrix using cofactor (Laplace) expansion. See every minor, sign, and cofactor term worked out step by step.
Open Cofactor Matrix Calculator Find the cofactor matrix of any 2x2, 3x3, or 4x4 matrix instantly. Shows minors, signs, the adjugate matrix, and a full step-by-step breakdown.
Open Column Space Calculator Find the column space (Col A) of any matrix up to 4x4 instantly. Shows basis vectors, rank, and dimension with a full step-by-step RREF solution.
Open Condition Number Calculator Calculate the condition number of a 2x2 or 3x3 matrix with four norm choices (1, 2, infinity, Frobenius). Shows matrix norm, inverse norm, and a worked step-by-step solution.
Open Corner Point Calculator: Linear Programming Feasible Region Solver Find all corner points of a linear program. Enter the objective function and constraints, get every vertex with its P value and the optimal solution shown step by step.
Open Cramer's Rule Calculator Solve any 2x2 or 3x3 linear system using Cramer's rule. Enter coefficients to get x, y, z with full determinant steps shown instantly.
Open Diagonalize Matrix Calculator Diagonalize any 2x2 or 3x3 matrix instantly. Get eigenvalues, eigenvectors, the P and D matrices, and a full step-by-step verification of A = PDP-1.
Open Eigenvalue and Eigenvector Calculator Find eigenvalues, eigenvectors, the characteristic polynomial, trace, determinant, and diagonalizability for any 2x2 or 3x3 matrix with step-by-step solutions.
Open Gauss-Jordan Elimination Calculator Solve 2x2, 3x3, or 4x4 linear systems with full Gauss-Jordan elimination. See every row operation, the RREF matrix, rank, nullity, and the solution instantly.
Open Gram-Schmidt Calculator Compute the orthogonal and orthonormal basis of up to 4 vectors in up to 4 dimensions using the Gram-Schmidt process, with a full step-by-step breakdown.
Open Hadamard Product Calculator Calculate the Hadamard (element-wise) product of two matrices instantly. Supports 1x1 to 4x4, shows step-by-step work, properties, and Frobenius norms.
Open Inverse Matrix Calculator Find the inverse of a 2x2 or 3x3 matrix instantly. Shows determinant, adjugate, step-by-step cofactor work, and whether the matrix is singular.
Open Linear Combination Calculator Solve any 2x2 system of linear equations using the elimination method. Get x and y instantly, with a full step-by-step worked solution and special-case detection.
Open Linear Independence Calculator Test whether a set of vectors is linearly independent or dependent. Uses Gaussian elimination to find rank, pivot count, and span dimension with step-by-step work.
Open LU Decomposition Calculator Compute the LU decomposition of any 2x2 or 3x3 matrix instantly. Shows L, U and P matrices, the determinant, and every elimination step. Free online tool.
Open Matrix Addition and Subtraction Calculator Add or subtract two matrices of any size from 2x2 to 4x4. Get the result matrix and a full element-by-element step-by-step solution instantly.
Open Matrix by Scalar Calculator Multiply a 2x2 matrix by any scalar instantly. Get the full result matrix plus a step-by-step solution showing every multiplication. Free online linear algebra tool.
Open Matrix Calculator Free matrix calculator for 2x2 and 3x3 matrices. Compute determinant, inverse, transpose, trace, adjugate, cofactors, and rank with step-by-step working.
Open Matrix Determinant Calculator Calculate the determinant of a 2x2, 3x3, or 4x4 matrix instantly. See cofactor expansion steps, trace, rank, and whether the matrix is invertible.
Open Matrix Multiplication Calculator Multiply two matrices (up to 4x4) instantly with full step-by-step dot-product working. Covers 2x2, 2x3, 3x3, 3x4, and more. Free, no sign-up required.
Open Matrix Norm Calculator Calculate all five standard matrix norms instantly: 1-norm, infinity norm, Frobenius norm, spectral 2-norm, and max norm for any matrix up to 4x4.
Open Matrix Power Calculator Raise any 2x2, 3x3, or 4x4 square matrix to a positive, zero, or negative integer power. See the resulting matrix, determinant, trace, and full step-by-step working.
Open Matrix Rank Calculator Find the rank of any matrix (up to 4x4) using Gaussian elimination. See every row operation, the pivot positions, nullity, and a plain-English interpretation.
Open Matrix Trace Calculator Calculate the trace of any square matrix up to 6x6 instantly. Shows diagonal elements, step-by-step working, key properties, and the eigenvalue-sum relationship.
Open Matrix Transpose Calculator Transpose any matrix up to 6x6 instantly. Enter integers, decimals, or fractions. See the transposed matrix, step-by-step working, and key properties.
Open Null Space Calculator Find the null space (kernel), nullity, and rank of any matrix up to 4x4. Shows RREF steps, basis vectors, and the parametric solution with full working.
Open Polar Decomposition Calculator Decompose any real 2x2 or 3x3 matrix into U (orthogonal) and P (positive semi-definite) factors. Shows singular values, step-by-step SVD work, and residual.
Open Pseudoinverse Calculator Calculate the Moore-Penrose pseudoinverse of any matrix online. Supports full column rank, full row rank, and SVD for rank-deficient cases, with step-by-step working.
Open QR Decomposition Calculator Factor any matrix A = QR instantly. Enter up to a 4x4 matrix and get the orthogonal Q matrix, upper-triangular R, step-by-step Gram-Schmidt work, and a verification check.
Open Reduced Row Echelon Form (RREF) Calculator Calculate the RREF or REF of any matrix step by step. Supports 2x2 to 4x5 matrices, exact fractions, and interprets unique, infinite, or no-solution systems.
Open Singular Values Calculator Calculate singular values of any 2x2 or 3x3 matrix with full SVD decomposition: U, Sigma, V-transpose, matrix rank, condition number, and Frobenius norm, step by step.
Open SVD Calculator - Singular Value Decomposition Compute the singular value decomposition A = U*Sigma*V^T of any 2x2 or 3x3 real matrix, with singular values, rank, condition number, and step-by-step working.
Open Tensor Product Calculator Compute the tensor product (Kronecker product) A x B of any two matrices. Shows the result matrix, block expansion steps, dimensions, Frobenius norm, and rank.
Open
2D Geometry 24
Area Calculator Calculate area and perimeter for 11 shapes: rectangle, square, triangle, circle, ellipse, trapezoid, sector, rhombus, and more. Optional cost estimate included.
Open Area of a Rectangle Calculator Calculate the area, perimeter, and diagonal of any rectangle. Enter length and width, or reverse-solve from area, perimeter, or diagonal. Metric and imperial units.
Open Area of Crescent Calculator Calculate the area of a crescent (lune) from two circle radii and their centre distance. Shows both lune areas, the lens overlap, and a step-by-step worked example.
Open Center of Mass Calculator Calculate the center of mass for up to 6 point masses in 1D, 2D, or 3D. Shows the weighted-average formula step by step with metric and imperial units.
Open Centroid Calculator Find the centroid (geometric center) of a triangle, polygon, or set of points. Enter vertex coordinates and get the x and y centroid instantly, with step-by-step math.
Open Conic Sections Calculator Calculate every property of any conic section: eccentricity, foci, vertices, directrix, asymptotes, latus rectum and more. Covers circles, ellipses, parabolas and hyperbolas.
Open Cross-Sectional Area Calculator Calculate cross-sectional area for 10 shapes: circle, pipe, rectangle, I-beam, T-section, C-channel, L-angle, and triangle. Metric/imperial with worked steps.
Open Cycloid Calculator Calculate cycloid arc length, area, hump length, height, perimeter, parametric coordinates, and radius of curvature for any rolling radius and angle.
Open Ellipse Calculator Calculate ellipse area, perimeter, eccentricity, focal distance, and latus rectum from semi-axes or full axes. Metric and imperial, step-by-step math shown.
Open Golden Rectangle Calculator Calculate all golden rectangle dimensions from one known value: long side, short side, diagonal, area, or perimeter. Includes unit switch and step-by-step math.
Open Hexagon Calculator Solve any regular hexagon from any measurement: side, area, perimeter, diagonal, apothem, or circumradius. Metric and imperial units. Step-by-step working shown.
Open Moment of Inertia Calculator Calculate the moment of inertia for 12 shapes across multiple axes. Supports metric and imperial units, hollow bodies, parallel-axis theorem, and torque output.
Open Octagon Calculator Solve a regular octagon from any known value: side, area, perimeter, any diagonal, circumradius, or apothem. Instant results plus an optional flooring cost estimate.
Open Orthocenter Calculator Find the orthocenter of any triangle from its three vertices. Instant result with step-by-step altitude equations, triangle type, and a live diagram.
Open Pentagon Calculator Solve any regular pentagon from one measurement: side, area, diagonal, height, apothem or circumradius. All outputs with step-by-step work.
Open Perimeter Calculator Perimeter calculator for 10 shapes: rectangle, square, triangle (SSS/SAS/ASA), circle, ellipse, trapezoid, parallelogram, rhombus, regular polygon, and custom sides.
Open Polygon Calculator Calculate area, perimeter, inradius, circumradius, interior angle, exterior angle, and diagonals of any regular polygon. Solve from any known dimension.
Open Quadrilateral Calculator Calculate the area, perimeter, and diagonals of any quadrilateral: rectangle, square, parallelogram, rhombus, trapezoid, kite, or any irregular shape.
Open Segment Addition Postulate Calculator Solve for any segment length with the segment addition postulate. Supports algebraic expressions (2x+3), shows step-by-step work, and checks collinearity.
Open Segment Area Calculator Calculate the area, arc length, chord, sagitta, and perimeter of a circular segment from radius plus angle, chord, or height. Instant results with worked steps.
Open Spiral Length Calculator Calculate the length and number of turns of an Archimedean (flat) or helical (3D) spiral. Enter outer diameter, inner diameter, and thickness for instant results.
Open Square Calculator: find A, P, d Calculate the area, perimeter, diagonal and side of a square from any one known measurement. Solve from side, area, perimeter or diagonal instantly.
Open Star Shape Calculator Calculate the area, perimeter, tip angle, and spike height of any regular star polygon. Supports 5- to 12-pointed stars with metric and imperial unit switches.
Open Trapezoid Calculator Solve any trapezoid from bases and height, all four sides, base angles, or reverse-solve for a missing side. Get area, perimeter, angles, diagonals, and median.
Open
3D Geometry 24
Cube Calculator Cube any number (n³) or enter one cube property and get the rest: edge, volume, surface area, face diagonal, and space diagonal with metric or imperial units.
Open Cube Calculator: Find Volume, Surface Area, and Diagonal Calculate the volume, surface area, face diagonal, and space diagonal of a cube. Enter any one value and solve the rest instantly, with step-by-step math and a visual diagram.
Open Ellipsoid Volume Calculator: Volume, Surface Area, and Equivalent Sphere Calculate the volume of any ellipsoid from its three semi-axes with step-by-step working, surface area (Thomsen formula), equivalent sphere radius, and unit switching.
Open Great Circle Calculator Calculate the great-circle distance, initial and final bearing, midpoint, and flight time between any two points on Earth using the Haversine formula.
Open Lateral Area of a Trapezoidal Prism Calculator Calculate the lateral and total surface area of a trapezoidal prism. Enter the four side lengths, trapezoid height, and prism length for step-by-step results.
Open Pyramid Angle Calculator Calculate all four angles of a regular right pyramid: alpha, beta, gamma, and delta. Also finds slant height, lateral edge, and apothem. Works for any polygon base.
Open Pyramid Volume Calculator Calculate pyramid volume, total surface area, lateral face area, slant height, and lateral edge for square, rectangular, triangular, or hexagonal pyramids.
Open Rectangular Prism Calculator Calculate the volume, total and lateral surface area, space diagonal, and face areas of a rectangular prism. Switch between metric and imperial units.
Open Right Circular Cone Calculator Calculate the volume, total surface area, lateral area, base area, and slant height of a right circular cone from any two known dimensions. Metric and imperial units.
Open Right Cylinder Calculator: Volume, Surface Area, Lateral Area Calculate volume, total surface area, lateral area, and base area of a right cylinder. Six solve modes, 7 length units, step-by-step math, and a shape diagram.
Open Right Rectangular Pyramid Calculator: A, V, A_l, A_b Calculate volume, total surface area, lateral surface area, base area, slant heights and lateral edge of a right rectangular pyramid instantly. Metric and imperial.
Open Slant Height Calculator Calculate the slant height of a cone or square pyramid instantly. Enter height and base to get slant height, or reverse-solve for height. Metric and imperial.
Open Sphere Calculator: Find V, A, d Solve any sphere property from a single known value. Enter radius, diameter, volume, surface area, or circumference and instantly get all the rest, with step-by-step working.
Open Surface Area Calculator Calculate total, lateral, and base surface area for 10 shapes: sphere, cube, cylinder, cone, box, hemisphere, capsule, pyramid, prism, and frustum.
Open Surface Area of a Hemisphere Calculator Calculate the curved, base, and total surface area of a hemisphere from any known value: radius, diameter, volume, or curved area. Metric and imperial units.
Open Surface Area of a Triangular Prism Calculator Calculate the total surface area, lateral area, and base area of a triangular prism. Choose from 4 triangle modes with step-by-step working and formulas.
Open Surface Area to Volume Ratio Calculator Calculate SA:V ratio for cubes, spheres, cylinders, cones, rectangular prisms, hemispheres, and capsules. Includes formulas, worked examples, and biology context.
Open Tetrahedron Volume Calculator Calculate volume, surface area, height, inradius, midsphere, circumradius, and surface-to-volume ratio for a regular tetrahedron. Includes reverse-solve from volume.
Open Torus Surface Area Calculator Calculate the surface area of a torus using tube radius and major radius, or inner and outer radii. Includes the formula, step-by-step working, and volume.
Open Torus Volume Calculator Calculate the volume and surface area of a torus instantly. Enter major and minor radii in metric or imperial units, see step-by-step working, and learn the formulas.
Open Triangular Prism Calculator Calculate the volume and surface area of any triangular prism. Five triangle input modes: base and height, right triangle, SSS, SAS, and ASA. Metric and imperial units.
Open Volume Calculator Volume calculator for 12 shapes: cube, box, sphere, cylinder, cone, capsule, ellipsoid, frustum, and more. Get surface area, litres, gallons, and step-by-step work.
Open Volume of a Hemisphere Calculator Calculate hemisphere volume, curved surface area, base area and total surface area from radius or diameter. Metric and imperial units, with step-by-step working.
Open Volume of a Trapezoidal Prism Calculator Calculate the volume, surface area, and lateral area of a trapezoidal prism instantly. Enter the two bases, height, leg lengths, and prism length. Metric or imperial.
Open
Trigonometry 22
Arccos Calculator (Inverse Cosine) Calculate arccos(x) instantly. Enter any value from -1 to 1 and get the inverse cosine in both degrees and radians, with steps, a reference table, and a curve visual.
Open Arcsin Calculator (Inverse Sine) Arcsin calculator: inverse sine in degrees and radians. Step-by-step working, cos and tan outputs, right-triangle mode, and a standard-values reference table.
Open Arctan Calculator (Inverse Tangent) Calculate arctan(x) instantly. Get the inverse tangent in degrees and radians, with rise/run input mode, step-by-step math, and a reference table of common values.
Open Cofunction Calculator Find cofunction identities for sin, cos, tan, cot, sec, and csc in degrees or radians. Get the complementary angle, exact value, and a step-by-step breakdown.
Open Cosecant Calculator Calculate the cosecant of any angle instantly. Enter degrees, radians, or pi multiples. See the formula, worked steps, the csc graph, and a full reference table.
Open Cosine Calculator Calculate cos(x) in degrees, radians, or milliradians. Reverse-solve with arccos. Solve triangles with the law of cosines. Step-by-step work included.
Open Cotangent Calculator Calculate the cotangent of any angle in degrees, radians, or pi-radians instantly. See the formula, worked steps, a reference table, and a graph of the cot function.
Open Double Angle Formula Calculator Calculate sin(2theta), cos(2theta), and tan(2theta) instantly. Supports degrees, radians, and pi-radians with step-by-step working and all three cosine variants.
Open Half Angle Calculator Calculate sin, cos, tan, csc, sec, and cot of half an angle using the half-angle identities. Enter degrees or radians and see the step-by-step working instantly.
Open Inverse Trigonometric Functions Calculator Calculate all six inverse trigonometric functions instantly. Enter a value to get arcsin, arccos, arctan, arccot, arcsec, and arccsc in both degrees and radians.
Open Law of Cosines Calculator Solve any triangle with the law of cosines. Find the missing side or angle, then get all three angles, area, perimeter, inradius, and circumradius in one step.
Open Law of Sines Calculator Solve any AAS, ASA or SSA triangle instantly. Get the missing side or angle, plus area, perimeter, inradius and circumradius. Ambiguous case flagged automatically.
Open Phase Shift Calculator Find the phase shift, amplitude, period and vertical shift of any sine or cosine function. Enter A, B, C, D and get instant results with step-by-step working.
Open Power Reducing Calculator Apply the power-reducing identities instantly. Enter any angle in degrees or radians and get sin², cos², tan², sin³, cos³, sin⁴ and cos⁴ with full step-by-step working.
Open Secant Calculator Calculate sec(x) for any angle in degrees, radians, or gradians. Includes inverse secant (arcsecant), step-by-step working, and a reference table of common angles.
Open Sine Calculator Calculate sin(x), cos(x), tan(x) and arcsin in degrees or radians. See exact values for 30-60-90 angles, quadrant info, and a full trig reference table.
Open Sum and Difference Identities Calculator Calculate sin(A+B), cos(A-B), tan(A+B) and all six trig functions using sum and difference identities. Enter two angles in degrees or radians with step-by-step working.
Open Tangent Calculator Calculate tan of any angle in degrees, radians, gradians, or milliradians. Get sin, cos, cot, sec, csc too, plus inverse tan (arctan) and step-by-step work.
Open Trig Identities Calculator Enter any angle to compute all six trig functions and verify Pythagorean, double-angle, half-angle, and sum/difference identities with full step-by-step workings.
Open Trigonometric Functions Calculator Calculate all six trig functions (sin, cos, tan, csc, sec, cot) and their inverses for any angle in degrees, radians, or gradians. Step-by-step work included.
Open Trigonometry Calculator Solve any right triangle from two values. Get all sides, angles, area, perimeter, altitude, and trig ratios with full step-by-step working in degrees or radians.
Open Unit Circle Calculator Find sine, cosine, tangent, cotangent, secant, cosecant, unit circle coordinates, reference angle, and quadrant for any angle in degrees or radians.
Open
Triangle 20
30-60-90 Triangle Calculator Solve a 30-60-90 triangle from any known value: short leg, long leg, hypotenuse, height, area, or perimeter. Get sides, altitude, inradius, circumradius, and area instantly.
Open 45-45-90 Triangle Calculator Solve a 45-45-90 triangle from any known value: leg, hypotenuse, altitude, area, or perimeter. Get all sides, inradius, circumradius, and step-by-step work.
Open Area of a Right Triangle Calculator Calculate the area of a right triangle from two legs, a leg and hypotenuse, a leg and angle, or hypotenuse and angle. Includes a full worked solution.
Open Circumscribed Circle Calculator Find the circumscribed circle radius, diameter, circumference and area for any triangle. Enter three side lengths in metric or imperial units and see every step.
Open Classifying Triangles Calculator Classify any triangle by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse). Get angles, area, perimeter, inradius and circumradius instantly.
Open Equilateral Triangle Calculator Solve any equilateral triangle property: enter the side, height, area, perimeter, inradius, or circumradius and get all six values instantly with step-by-step work.
Open Heron's Formula Calculator Calculate the area of any triangle from its three sides using Heron's formula. Shows altitudes, interior angles, inradius, and circumradius with step-by-step working.
Open Hypotenuse Calculator Find the hypotenuse from two legs, one leg plus an angle, or a special triangle. Also outputs both angles, altitude, perimeter and area instantly.
Open Isosceles Triangle Calculator Calculate area, height, perimeter, base angles, apex angle, inradius, and circumradius of an isosceles triangle. Choose from 5 solve modes.
Open Perimeter of a Triangle Calculator Calculate the perimeter of any triangle using three sides (SSS), two sides and an angle (SAS), or one side and two angles (ASA). Shows all steps and the semi-perimeter.
Open Pythagorean Theorem Calculator Solve any right triangle: enter any two of three sides (a, b, c) to find the missing side, both angles, area, perimeter, and altitude. Unit switching included.
Open Pythagorean Triples Calculator Check if three integers form a Pythagorean triple or generate one with Euclid's formula. Finds primitives, scaling factors, area, perimeter, and step-by-step math.
Open Right Triangle Calculator Solve any right triangle from any two values. Get sides, angles, area, perimeter, semiperimeter, all three altitudes, inradius, and circumradius instantly.
Open Right Triangle Side and Angle Calculator Solve any right triangle instantly. Enter two known values to find all sides, both acute angles, altitude, area, and perimeter with step-by-step working.
Open Similar Triangles Calculator Check if two triangles are similar by SSS, SAS, or AA. Find any missing side, scale factor, area ratio, and perimeter ratio with full step-by-step working.
Open Special Right Triangles Calculator Solve any special right triangle: 45-45-90, 30-60-90, 3-4-5, and more. Enter one side to get all sides, angles, area, and perimeter instantly with full steps.
Open Triangle Angle Calculator Solve any triangle. Enter any 3 known values (sides and angles) to get all missing angles, sides, area, perimeter, inradius, and circumradius with steps.
Open Triangle Area Calculator Find any triangle's area from base-height, three sides (Heron's), SAS, ASA, or equilateral shortcut. Switch metric or imperial units and see every step.
Open Triangle Height Calculator Calculate the height (altitude) of any triangle. Choose from four methods: three sides, area and base, two sides and angle, or equilateral formula. All three altitudes shown.
Open Triangle Inequality Theorem Calculator Check whether three side lengths form a valid triangle. See which inequalities pass or fail, find the valid range for any missing side, and get a step-by-step proof.
Open
Fractions 19
Adding Fractions Calculator Add or subtract up to 4 fractions at once. Finds the LCD automatically, shows every step, and returns a simplified fraction, mixed number, and decimal.
Open Comparing Fractions Calculator Compare two fractions or mixed numbers instantly. See the result as <, >, or =, with decimal values, the LCD method, cross-multiplication, and full worked steps.
Open Decimal to Fraction Calculator Convert any decimal to a simplified fraction: terminating, repeating, or rounded to nearest. Full step-by-step work shown. Includes reverse fraction-to-decimal mode.
Open Dividing Fractions Calculator Divide any two fractions, mixed numbers, or whole numbers instantly. See the full step-by-step solution using Keep, Change, Flip, simplified to lowest terms.
Open Equivalent Fractions Calculator Generate equivalent fractions, simplify to lowest terms, check if two fractions are equivalent, or solve for a missing numerator or denominator. Free, instant.
Open Fraction Calculator Add, subtract, multiply, or divide two fractions. Supports mixed numbers, shows LCM and GCF, gives the result as a mixed number, decimal, and percentage.
Open Fraction Exponent Calculator Calculate any fractional exponent x^(n/d) instantly. See both methods, a step-by-step breakdown, and worked examples. Handles negative and fractional bases.
Open Fraction to Decimal Converter Convert any fraction or mixed number to a decimal instantly. Shows long-division steps, detects repeating decimals, and sets rounding precision from 0 to 10 places.
Open Golden Ratio Calculator Split any length by phi, find golden rectangle dimensions, explore the golden angle (137.5 deg), and see the Fibonacci convergence to phi = 1.6180.
Open Improper Fraction to Mixed Number Calculator Convert any improper fraction to a mixed number instantly. Shows the whole part, remainder, simplified fraction, decimal, and full step-by-step working.
Open LCD Calculator - Least Common Denominator Find the least common denominator of up to 6 fractions instantly. See equivalent fractions, prime factorization, and a full step-by-step solution.
Open Lowest Term Calculator Reduce any fraction to its lowest terms with step-by-step GCD working. Supports proper fractions, improper fractions, and mixed numbers in one click.
Open Mixed Number Calculator Add, subtract, multiply, or divide mixed numbers and convert between improper fractions and mixed numbers. Step-by-step work shown, results fully simplified.
Open Mixed Number to Improper Fraction Calculator Convert any mixed number to an improper fraction instantly. See the step-by-step formula, simplify the result, and check the decimal equivalent.
Open Multiplying Fractions Calculator Multiply two or three fractions or mixed numbers instantly. Get the simplified fraction, mixed number, and decimal result, plus a full step-by-step breakdown.
Open Proportion Calculator Solve for any unknown in a proportion a/b = c/d. Supports direct and inverse proportions, scale factor, percent difference, and step-by-step cross-multiplication work.
Open Ratio Calculator Simplify ratios, solve any proportion for a missing value, scale a ratio, or split into 3 parts. See decimal, percentage, and fraction equivalents instantly.
Open Simplify Fractions Calculator Reduce any fraction to lowest terms instantly. Get the simplified fraction, decimal, percentage, mixed number, and equivalent fractions with step-by-step work shown.
Open Unit Rate Calculator Find the unit rate for any quantity in one click. Compare two options side-by-side to find the better deal, see a multiples table, and get step-by-step working.
Open
Exponents And Logarithms 17
Antilog Calculator - Antilogarithm Calculate the antilogarithm instantly for any base: base 10, natural log (e), base 2, or a custom base. See the formula, worked steps, and a curve visual.
Open Change of Base Formula Calculator Convert logarithms from any base to base 10, base e, or any custom base using the change of base formula. Shows step-by-step work and the full derivation.
Open Condense Logarithms Calculator Condense two log terms into one instantly. Enter coefficients, arguments, and base - get the condensed form, step-by-step rule breakdown, and numeric result.
Open Dividing Exponents Calculator Divide exponents instantly: enter any two bases and exponents to apply the quotient rule or get a numerical answer, with a full step-by-step worked solution.
Open Dividing Radicals Calculator Divide two radical expressions instantly. Enter coefficients, radicands, and indices for each radical to get the fully simplified quotient with step-by-step work shown.
Open e Calculator - eˣ, Euler's Number Raised to Power x Calculate e raised to the power x (eˣ) instantly. Get the exact result, Taylor series steps, natural log inverse, and a live curve chart of the exponential function.
Open Expanding Logarithms Calculator Expand any logarithm instantly using the product, quotient, or power rule. Enter your base and arguments to see a full step-by-step worked solution.
Open Exponent Calculator Calculate bⁿ, solve for the base, or find an unknown exponent. Supports e as base, negative and fractional exponents, laws of exponents, and a step-by-step breakdown.
Open Exponential Form Calculator Convert numbers to exponential form in four modes: prime factorization, scientific notation, log to exponential, and exponential to logarithm. Shows every step.
Open Exponential Function Calculator Evaluate any exponential function or solve for its parameters from two points. Supports four forms including natural base, with step-by-step working and a growth curve chart.
Open Exponential Growth Calculator Calculate exponential growth or decay. Solve for final value, initial value, growth rate, or time. Supports discrete and continuous compounding with step-by-step work.
Open Log Base 2 Calculator Calculate log base 2 (binary logarithm) instantly. Enter x to find log2(x) or enter the result to reverse-solve for x. Includes steps, curve, and a powers-of-2 table.
Open Log Calculator (Logarithm) Calculate any logarithm: enter a number and base to find log_b(x), compute the antilog, or solve for an unknown base. Includes log rules and a worked example.
Open Multiplying Exponents Calculator Multiply exponents instantly: same base, same exponent, and power-of-a-power rules. See the formula, step-by-step working, and the numeric result.
Open Multiplying Radicals Calculator Multiply two radical expressions instantly. Enter coefficients, radicands, and root indices. Get step-by-step simplification using the product rule and LCM method.
Open Natural Log Calculator Calculate ln(x), reverse-solve x from ln(x), convert to any log base, and find doubling time or half-life. Includes steps, a chart, and a reference table.
Open Negative Log Calculator Calculate the negative logarithm (-log) of any positive number in any base. Includes pH, decibel and entropy formulas, step-by-step working, and a curve visual.
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Percentages 15
Average Percentage Calculator Calculate the average of multiple percentages instantly. Choose simple or weighted average, see a step-by-step breakdown, and get the formula explained.
Open Decimal to Percent Converter Convert any decimal to a percentage (or percent back to a decimal) instantly. See the formula, worked steps, and a quick-reference table for common values.
Open Doubling Time Calculator Calculate doubling time from a growth rate or from initial and final values. Continuous and discrete growth models, Rule of 70/72 comparison, and step-by-step math.
Open Fraction to Percent Calculator Convert any fraction or mixed number to a percent instantly. Supports reverse mode (percent to fraction), rounding control, and step-by-step work shown.
Open Percent Error Calculator Calculate percent error, absolute error, and relative error. Reverse-solve for the experimental or theoretical value when the percent error is known.
Open Percent to Goal Calculator Calculate the percentage of any goal you have reached. Enter your progress and target, get percent achieved, amount remaining, and a performance band.
Open Percentage Calculator Five percentage calculators in one: percent of a number, ratio, percent change, reverse-solve the whole, and apply a percent increase or decrease.
Open Percentage Change Calculator Calculate percentage increase or decrease between two values, or reverse-solve to find the original or new value from a known percent change.
Open Percentage Decrease Calculator Calculate percentage decrease, find the new value after a % drop, or reverse-solve the original. Cost-saving estimate, show-your-work steps, and real examples.
Open Percentage Difference Calculator Find the percentage difference between two numbers with step-by-step working. Also shows percentage change, absolute difference, and the midpoint used in the formula.
Open Percentage Increase Calculator Calculate percentage increase from old to new, find the new value after a % rise, or reverse-solve the original. Steps, chart, and real-world examples included.
Open Percentage of a Percentage Calculator Find the combined effect of two percentages applied in sequence. See the cumulative percentage, intermediate value, and final value instantly with worked steps.
Open Percentage Point Calculator Calculate the percentage point (pp) difference and the relative percentage change between two percentages instantly, with a worked breakdown and real-world examples.
Open Relative Change Calculator Calculate relative change and percentage change between any two values. Shows the formula, step-by-step working, handles negative numbers, and covers reverse-solve.
Open Slope Percentage Calculator Convert slope between percent grade, angle in degrees, rise over run, and 1:N ratio. Covers roads, ramps, roofs and trails with a quick reference table.
Open
Binary 14
AND Calculator - Bitwise AND Operation Calculate the bitwise AND of two integers instantly. Enter decimal, binary (0b), or hex (0x) values and get results in all four bases with a step-by-step bit-by-bit breakdown.
Open Binary Addition Calculator Add two binary numbers instantly, see the column-by-column carry process, decimal and hex equivalents, and a full step-by-step worked solution.
Open Binary Calculator Perform binary arithmetic and bitwise operations with selectable 4/8/16/32-bit width. Outputs binary, decimal, octal, hex, and signed value instantly.
Open Binary Division Calculator Divide two binary numbers instantly. Get the quotient and remainder in binary and decimal, with a full long-division step-by-step breakdown.
Open Binary Fraction Converter Convert decimal fractions to binary and binary fractions to decimal in one click. See step-by-step working, repeating pattern detection, and conversion error.
Open Binary Multiplication Calculator Multiply two binary numbers instantly. Get the product in binary, decimal, and hex with a full long-multiplication step-by-step breakdown and partial products.
Open Binary Subtraction Calculator Subtract two binary numbers instantly using the borrow method or two's complement. See step-by-step column work, decimal equivalents, and overflow detection.
Open Bit Shift Calculator Shift bits left or right with decimal, binary, hex, or octal input. Shows all four output bases, signed and unsigned values, and step-by-step work.
Open Bitwise Calculator Free bitwise calculator for AND, OR, XOR, NOT, NAND, NOR, XNOR, left shift and right shift. Supports binary, octal, decimal and hex with a per-bit breakdown.
Open NOR Calculator Calculate bitwise NOR for any two integers in binary, octal, decimal, or hex. Flip to logic mode to see a full NOR truth table for 2 to 4 inputs with step-by-step work.
Open One's Complement Calculator Find the one's complement of any decimal, binary, or hex number instantly. Choose 4, 8, 16, or 32-bit width. Shows results with step-by-step working.
Open OR Calculator (Bitwise) Compute the bitwise OR of two integers in decimal, binary, hexadecimal, or octal. See the result in all four bases with a bit-by-bit working and truth table.
Open Two's Complement Calculator Convert any integer to two's complement binary instantly. Supports 4 to 64-bit widths, decimal, binary and hex input, one's complement, and step-by-step working.
Open XOR Calculator Compute bitwise XOR for any two integers across binary, decimal, hex, and octal. See a step-by-step bit-level breakdown, truth table, and Hamming weight of the result.
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Circle 12
Arc Length Calculator Calculate arc length, chord, sector area, sagitta and perimeter from radius and central angle in degrees or radians. Reverse-solve for radius or angle.
Open Area of a Circle Calculator Find circle area from radius, diameter, circumference, or area. Includes sector area, annulus area, unit switch, exact-pi output, and a full worked solution.
Open Circle Calculator Solve any circle from radius, diameter, circumference, or area. Get all four properties, exact pi form, sector area and arc length in any unit.
Open Circle Theorems Calculator Calculate inscribed angles, central angles, arc lengths, chord lengths, cyclic quadrilateral angles, and secant-tangent relationships with step-by-step working.
Open Circumference Calculator Find circumference, area, radius, diameter, arc length, and sector area from any one circle measurement. Metric and imperial units, with step-by-step working.
Open Coin Rotation Paradox Calculator Calculate how many times a rolling coin rotates around a fixed coin. Covers external and internal rolling, any radius ratio, with step-by-step math and worked examples.
Open Equation of a Circle Calculator Find the equation of a circle in standard, general, and parametric form. Enter center and radius, three points, or general-form coefficients for instant step-by-step results.
Open Sector Area Calculator Calculate sector area, arc length, chord length, and segment area from radius and central angle. Supports degrees or radians, metric or imperial, and reverse-solve.
Open Semicircle Area Calculator Calculate semicircle area, perimeter, arc length, radius and diameter instantly. Enter any one value and get all the rest, with step-by-step working.
Open Square in a Circle Calculator Calculate the largest square inside a circle, largest circle inside a square, or find equal-area equivalents. Instant results with step-by-step formulas.
Open String Girdling Earth Calculator: Gap and Extra Length Calculate the extra string needed to raise a rope around Earth by any gap, or find the gap from the extra length. Formula, steps, and worked examples included.
Open Tangent of a Circle Calculator Calculate the tangent length from an external point to a circle, the angle between tangents, and two-circle external and internal tangent lengths. Full worked steps.
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Sequences 11
Arithmetic Sequence Calculator Find the nth term, partial sum, and any missing value of an arithmetic sequence. Reverse-solve for a1, d, or n, and see a list of every term with steps.
Open Collatz Conjecture Calculator Enter any positive integer to generate its full Collatz (hailstone) sequence, count total steps to reach 1, find the peak value, and see a step-by-step chart.
Open Convolution Calculator Compute discrete convolution of two sequences instantly. Choose linear or circular mode, see each output term worked out step by step, and read the result table.
Open Fibonacci Calculator Find any Fibonacci number with exact big-integer math. List the sequence, explore negative indices, use custom seeds, and see the golden ratio converge.
Open Geometric Sequence Calculator Find the nth term, partial sums, infinite sum, and full term list for any geometric sequence. Supports reverse-solve: enter two terms to find the ratio and first term.
Open Harmonic Number Calculator Calculate the nth harmonic number instantly. Shows the exact fraction, decimal, asymptotic approximation, generalized H(n,m), step-by-step partial sums, and a growth chart.
Open Lagrange Error Bound Calculator Calculate the Lagrange error bound for a Taylor polynomial instantly. Enter the degree, evaluation point, center, and max derivative to find the maximum approximation error.
Open Pascal's Triangle Calculator Generate Pascal's triangle up to any row, find any binomial coefficient C(n,k), or look up the row sum. Step-by-step working shown for every calculation.
Open Sequence Calculator Find the nth term and sum of an arithmetic, geometric, or Fibonacci sequence. Shows step-by-step work, lists the first N terms, and plots the sequence.
Open Sum of a Linear Number Sequence Calculator Find the sum, final term, and nth term of any arithmetic sequence. Enter the first term, common difference, and number of terms for instant results.
Open Sum of Series Calculator Calculate the sum of arithmetic, geometric (finite and infinite), harmonic, square, and cube number series. Shows the formula, worked steps, and a cumulative-sum chart.
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Angle 7
Angle Between Two Vectors Calculator Find the angle between two vectors in 2D or 3D using the dot product formula. Get degrees, radians, and a full step-by-step breakdown instantly.
Open Central Angle Calculator Calculate the central angle from arc length and radius, find arc length from an angle, or convert between inscribed and central angles. Degrees, radians, metric, imperial.
Open Clock Angle Calculator Find the angle between clock hands at any time, with a step-by-step breakdown, both sweep directions, each hand position, and a reverse-solve mode.
Open Complementary Angles Calculator Find the complementary angle for any angle in degrees or radians. Check whether two angles are complementary and see all six trig cofunctions explained.
Open Coterminal Angle Calculator Find positive and negative coterminal angles instantly. Works in degrees and radians. Shows the principal angle, reference angle, quadrant, and step-by-step work.
Open Reference Angle Calculator Find the reference angle for any angle in degrees or radians. Shows the quadrant, step-by-step formula, trig signs, and common angle equivalents instantly.
Open Supplementary Angles Calculator Find the supplementary angle in degrees or radians instantly. Enter one angle and get the missing angle, verify two angles are supplementary, and see trig relationships.
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What Math Calculators Are Used For
Math calculators cover the full range of school and real-world mathematics, from basic arithmetic all the way through algebra, geometry, trigonometry, and introductory calculus. Whether you are checking a homework answer, verifying a quick estimate at work, or brushing up on concepts you have not touched in years, these tools give you instant, step-by-step results that show the underlying logic rather than just printing a number.
Common Uses and Real-Number Examples
- Geometry and area problems. If you are planning a circular garden with a radius of 6 feet, the area formula A = π r² gives you roughly 113 square feet. A geometry calculator walks through that multiplication automatically and can also return circumference, diameter, and sector area for the same circle.
- Solving algebraic equations. Say you need to find x in 3x + 12 = 39. An algebra calculator isolates x step by step: subtract 12 from both sides to get 3x = 27, then divide by 3 to reach x = 9. Watching the steps reinforces the method so you can repeat it on similar problems.
- Trigonometry for angles and distances. If a ladder 10 feet long leans against a wall and the base sits 4 feet from the wall, you can use the inverse cosine (cos⁻¹ of 4/10) to find the angle is about 66 degrees. Trig calculators handle sine, cosine, tangent, and their inverses in both degrees and radians.
- Calculus concepts explained numerically. Derivative and integral calculators show you the rate of change of a function or the area under a curve, with the rules applied step by step. For example, the derivative of f(x) = 4x³ is 12x², which the power rule produces automatically.
Key Concepts in Plain Language
Most math formulas are shorthand for a logical process. The Pythagorean theorem (a² + b² = c²) simply states that in a right triangle, the squares of the two shorter sides add up to the square of the longest side. The quadratic formula finds the values of x that make ax² + bx + c equal zero by combining a few arithmetic operations in a specific order. Understanding what the formula is doing, not just memorizing it, is what calculators help reinforce when they show intermediate steps.
What to Look For When Using These Tools
Always check the units and number format a calculator expects. Some tools work in degrees while others default to radians for trigonometry. Confirm whether a calculator uses the standard order of operations (parentheses first, then exponents, then multiplication and division, then addition and subtraction) so your input matches what the tool expects. When a result looks surprising, re-enter the numbers one at a time and compare each intermediate value to catch where an input error crept in.