Ratio Calculator
A ratio states how two (or three) quantities compare to each other. This calculator covers every common ratio task: simplify to lowest terms, solve a proportion A:B = C:D for any missing value, normalize to 1:n or n:1, scale a ratio by a multiplier, or break a 3-part ratio into percentages and fractions.
Formula
Worked example
12:8 simplifies to 3:2 (GCD = 4). As a decimal: 12/8 = 1.5. For proportion 12:8 = 6:D: D = 8*6/12 = 4. For 3-part 3:2:1: total = 6, shares are 50% / 33.3% / 16.7%.
How this calculator works
The calculator has four modes. Simplify divides both terms by their greatest common divisor (GCD) using the Euclidean algorithm. Solve proportion applies cross-multiplication: in A:B = C:D, the product of the means (B*C) equals the product of the extremes (A*D), so any one of the four terms can be recovered from the other three. Scale multiplies both terms of a ratio by a constant factor to enlarge or shrink it while keeping the proportion identical. 3-part mode handles ratios like 2:3:1 by summing all three parts, simplifying with the three-way GCD, and reporting each part as a percentage and fraction of the whole.
Simplifying a ratio and finding the GCD
A ratio A:B is in its simplest (lowest) form when no positive integer greater than 1 divides both A and B evenly. The GCD is found with the Euclidean algorithm: repeatedly replace the larger number with the remainder when the larger is divided by the smaller, until the remainder is zero. For example, gcd(12, 8) = gcd(8, 4) = gcd(4, 0) = 4, so 12:8 reduces to 3:2. When inputs are decimals rather than integers, both terms are scaled to integers before applying the algorithm, then the GCD of the scaled values is used.
Solving proportions by cross-multiplication
A proportion A:B = C:D means the fraction A/B equals C/D. Cross-multiplying gives A*D = B*C. Rearranging: D = B*C/A, C = A*D/B, B = A*D/C, A = B*C/D. This method is used to scale recipes (double a 2:1 mix to 4:2), read maps (1:50000 scale means 1 cm = 500 m), and solve unit-rate problems in finance and science. Enter any three of the four values and select which one to solve for.
Normalizing to 1:n or n:1
A ratio can be expressed in a unit form by dividing both terms by one of them. 1:n form divides both by A, giving 1 : (B/A), useful when comparing multiple ratios on a common base of 1 unit of the first quantity. n:1 form divides both by B, giving (A/B) : 1, convenient when the second quantity is the reference (such as a mixing ratio expressed per unit of solvent). Both forms are mathematically equivalent to the simplified form but are easier to compare across different ratios.
Scaling a ratio
Scaling multiplies both terms by the same positive number, producing an equivalent ratio. For example, 3:2 scaled by 4 gives 12:8, which is exactly 12:8 in its original form. Scaling up is used in construction (drawing plans at scale 1:20 means each metre on site is 5 cm on the plan) and cooking (if a recipe uses a 1:3 ratio of oil to vinegar, scaling by 6 gives 6 tablespoons oil to 18 tablespoons vinegar). To shrink a ratio, use a multiplier less than 1 (for example 0.5).
3-part ratios and splitting wholes
Three-part ratios appear whenever something is split into three groups, such as concrete mix (1 part cement : 2 parts sand : 3 parts aggregate), paint blending (pigment : binder : thinner), or profit splits among three partners. The share of each part in the whole is its term divided by the sum of all three terms. For A:B:C = 2:3:1, the total is 6, so A is 2/6 = 33.3%, B is 3/6 = 50%, and C is 1/6 = 16.7%. Simplification for three-part ratios divides all three terms by their three-way GCD.
Common ratios and their simplified forms
| Use case | Original ratio | Simplified | Decimal |
|---|---|---|---|
| Concrete (C20 mix) | 1 : 2 : 4 | 1 : 2 : 4 | 1.0 |
| Full HD display | 1920 : 1080 | 16 : 9 | 1.778 |
| Golden ratio (approx) | 1618 : 1000 | 809 : 500 | 1.618 |
| Vinegar dressing | 1 : 3 (oil : vinegar) | 1 : 3 | 0.333 |
| Map (1:50000) | 1 : 50000 | 1 : 50000 | 0.00002 |
| Mortar (1:4) | 1 : 4 | 1 : 4 | 0.25 |
| Profit split (2:3:5) | 2 : 3 : 5 | 2 : 3 : 5 | 0.4 / 0.6 / 1.0 |
| Aspect 4:3 | 4 : 3 | 4 : 3 | 1.333 |
Frequently encountered ratios across cooking, design, construction, and finance.
Frequently asked questions
What is the difference between a ratio and a proportion?
A ratio is a comparison of two quantities, written as A:B or A/B. A proportion is a statement that two ratios are equal: A:B = C:D. Ratios describe a relationship; proportions use that relationship to find a missing value.
How do I simplify a ratio that contains decimals?
Multiply both terms by the power of ten that clears the decimals, then find the GCD of the resulting integers and divide. For example, 0.5 : 1.5 becomes 5 : 15 (multiply by 10), then GCD(5,15) = 5, giving 1 : 3. This calculator handles that conversion automatically.
How do I find a missing value in A:B = C:D?
Cross-multiply: the product of the means equals the product of the extremes (A*D = B*C). Solve for the unknown: D = B*C/A, C = A*D/B, B = A*D/C, or A = B*C/D. Select "Solve proportion" mode, choose which term to solve for, then enter the other three.
What does 1:n form mean?
1:n (also called unit ratio) expresses a ratio so that the first term equals 1. Divide both terms by A to get 1 : (B/A). For example, 3:2 becomes 1 : 0.667. This form is useful when comparing multiple ratios at a glance, because the n values can be compared directly.
How do I split an amount in a given ratio?
Add the ratio terms to get the number of parts, divide the total amount by that number to get one part, then multiply each term by one part. For a 2:3 split of 500: total parts = 5, one part = 100, shares are 200 and 300. Use the 3-part mode if there are three groups.
Can I use this calculator for 3-part ratios like concrete mixes?
Yes. Select the "3-part ratio A:B:C" mode and enter all three terms. The calculator simplifies the ratio, shows each part as a percentage of the whole, and expresses each part as a fraction. Standard concrete mixes such as 1:2:3 (cement:sand:aggregate) and 1:2:4 are common examples.