Dimensions of a Rectangle Calculator
Enter any two rectangle measurements and this calculator instantly finds the rest: length, width, area, perimeter, and diagonal. Choose a solve mode that matches what you already know, switch between metric and imperial units, and see the step-by-step working below the result.
How this calculator works
A rectangle has four right-angle corners, two pairs of equal opposite sides, and two equal diagonals. Any two independent measurements fully determine the shape. This calculator offers five solve modes: Length + Width (the most common case), Area + Perimeter (useful when you have site survey data), Area + One Side (handy for flooring and tiling), Perimeter + One Side (common in framing), and Diagonal + One Side (useful when only the diagonal can be measured). Once the two known values are entered the calculator finds all remaining properties instantly.
Rectangle formulas
All four formulas follow from the basic geometry. Area (A) equals length times width: A = l x w. Perimeter (P) equals the sum of all four sides: P = 2l + 2w, or equivalently 2(l + w). The diagonal (d) is the hypotenuse of the right triangle formed by the two sides, so by the Pythagorean theorem: d = sqrt(l^2 + w^2). The angle the diagonal makes with the longer side is angle = arctan(w / l), measured in degrees. When you know the area and perimeter, the side lengths come from a quadratic equation: the solutions are (P/2 + sqrt((P/2)^2 - 4A)) / 2 for the longer side and (P/2 - sqrt((P/2)^2 - 4A)) / 2 for the shorter side. A valid rectangle requires P^2 >= 16A, otherwise the perimeter is too short to enclose the given area.
Practical uses for rectangle dimension calculations
Flooring and tiling: enter the room length and width in Area + One Side mode to find how many square metres or square feet of material you need. Framing and fencing: enter the total perimeter and one known post-to-post span to find the perpendicular span. Screen and print layouts: verify that your canvas or print matches the intended aspect ratio. Construction: confirm that a rectangular slab has right-angle corners by checking that two measured diagonals match the computed value. If the diagonals differ, the shape is a parallelogram, not a rectangle. Photography and film: the diagonal of a sensor or screen determines the field of view, so the Diagonal + One Side mode gives you the missing sensor dimension when only the crop-factor diagonal is quoted.
Aspect ratio and the golden rectangle
The aspect ratio is the ratio of the longer side to the shorter side, written as l:w. Common ratios include 16:9 (widescreen video), 4:3 (classic TV and photography), 3:2 (35 mm film and many digital cameras), and 1.414:1 (the ISO A-series paper standard, where the ratio is the square root of 2, a property that means folding the sheet in half gives another sheet of the same proportions). The golden rectangle has an aspect ratio of approximately 1.618:1, often called phi. It has appeared in art and architecture for centuries because many observers find it pleasing to look at. To check whether your rectangle is close to golden, divide the longer side by the shorter: if the result is near 1.618, you have a golden rectangle.
Common rectangle formats and their dimensions
| Format | Typical dimensions | Aspect ratio | Notes |
|---|---|---|---|
| A4 paper | 297 mm x 210 mm | 1.414:1 | ISO 216 standard |
| Letter paper | 11 in x 8.5 in | 1.294:1 | North American standard |
| HD screen | 1920 px x 1080 px | 16:9 | HDTV widescreen |
| 4K screen | 3840 px x 2160 px | 16:9 | Ultra-HD display |
| Golden ratio | 1.618 x 1 | 1.618:1 | Phi, aesthetically pleasing |
| Standard door | 80 in x 36 in | 2.222:1 | US residential |
| Queen mattress | 80 in x 60 in | 4:3 | US standard |
| Football field | 360 ft x 160 ft | 9:4 | NFL regulation |
Standard dimensions used in construction, screens, and print. Use the Solve mode to verify any format.
Frequently asked questions
How do I find the dimensions of a rectangle from its area and perimeter?
Set up two equations: A = l x w and P = 2(l + w). From the second, l + w = P/2. Substituting gives the quadratic l^2 - (P/2)l + A = 0. Solve with the quadratic formula: the larger root is the length and the smaller root is the width. This calculator does the algebra for you in the Area + Perimeter mode. Note that a valid rectangle requires the perimeter squared to be at least 16 times the area.
What is the diagonal of a rectangle?
The diagonal is the straight line connecting two opposite corners. Because each corner is a right angle, the diagonal is the hypotenuse of a right triangle formed by the two sides. The length is given by the Pythagorean theorem: d = sqrt(l^2 + w^2). Both diagonals of any rectangle are equal in length, which is a useful check when setting out a rectangular room or slab: if your two measured diagonals agree, the corners are truly 90 degrees.
How do I find the length and width of a rectangle from its area alone?
You cannot: area by itself does not uniquely define a rectangle. A 40 m^2 area could come from a 2 x 20 m room, an 8 x 5 m room, or countless other combinations. You need one extra piece of information: a side length, the perimeter, or the diagonal. Enter that second value in the matching solve mode above.
Is a square a rectangle?
Yes. A square is a special rectangle where all four sides are equal. Every formula on this page applies to a square: area = s^2, perimeter = 4s, and diagonal = s x sqrt(2). If you enter equal length and width in the Sides mode, the calculator gives the correct square results.
What is the aspect ratio of a rectangle?
The aspect ratio expresses how wide a rectangle is relative to its height, written as length:width or as a decimal. A 16:9 rectangle is 16 units wide for every 9 units tall, or about 1.778 times as wide as it is tall. Aspect ratio does not tell you the size of the rectangle, only its proportions.
Can the perimeter be too small for a given area?
Yes. For a given area A, the minimum possible perimeter is 4 x sqrt(A), which occurs when the shape is a square. If you enter an area and a perimeter smaller than 4 x sqrt(A), no real rectangle exists and the calculator returns no result. The mathematical condition is P^2 >= 16A.
How do I verify that a room is rectangular?
Measure both diagonals. If the two diagonals are equal in length, all four corners are 90 degrees and the room is a true rectangle. If they differ, the room is a parallelogram or an irregular quadrilateral. Once you know the diagonals agree, use the Diagonal + One Side mode with one wall length to find the perpendicular wall length without measuring across the room.