Ratio Calculator
Simplify a ratio to its lowest terms and optionally scale it. Enter A and B to see the simplified ratio, then enter a target value for A or B to find the corresponding scaled figure.
How Ratio Calculator works
What is a ratio?
A ratio compares two quantities and shows how much of one there is relative to the other. Written as A:B (or A/B), it can represent anything from ingredients in a recipe to the width-to-height relationship of a screen. Unlike fractions, ratios are not necessarily parts of a whole — 2:3 does not mean two-thirds of something.
Simplifying a ratio
To simplify a ratio, divide both sides by their greatest common divisor (GCD). For example, 12:18 — GCD(12, 18) = 6, so the simplified ratio is 2:3. A simplified ratio is in its lowest terms when the two numbers share no common factor other than 1. This makes the relationship clearer and easier to work with.
Scaling a ratio
Scaling a ratio means finding equivalent values that maintain the same proportion. If the ratio of flour to sugar is 3:1, and you want to use 450g of flour, the sugar needed is 450 × (1/3) = 150g. Scaling is used in cooking, map reading, architectural drawings, and any situation where proportions must be preserved when quantities change.
Ratio versus fraction versus percentage
A ratio (2:3) and a fraction (2/5) express the same relationship differently. In the ratio 2:3, there are 5 total parts; the first represents 2/5 and the second 3/5 of the whole — or 40% and 60% respectively. Ratios show relative amounts; fractions show a part of a whole; percentages scale to 100. Each form is useful in different contexts.
Frequently asked questions
How do I simplify 24:36?
Find the GCD of 24 and 36. GCD(24, 36) = 12. Divide both sides by 12: 24÷12 = 2, 36÷12 = 3. So 24:36 simplifies to 2:3.
What is the difference between a ratio and a fraction?
A fraction (a/b) represents a part of a whole. A ratio (a:b) compares two quantities without necessarily implying a whole. For example, a ratio of 1:3 means for every 1 unit of A there are 3 of B. As a fraction of the total (4 parts), A is 1/4. The ratio can be converted to a fraction, but they answer slightly different questions.
How do I scale a ratio?
Multiply or divide both sides of the ratio by the same number to maintain proportion. To scale 3:4 so that A = 9, multiply both by 3: 9:12. To find what B is when A = 5 in the ratio 2:7, calculate 5 × (7/2) = 17.5, so B = 17.5.
Can ratios have more than two parts?
Yes — ratios can compare three or more quantities (e.g., 1:2:3 for a three-way split). This calculator handles two-part ratios. For three-part ratios, you can simplify by dividing all parts by the GCD of all three numbers.
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