Ratio calculator
Simplify a ratio, solve a proportion, scale a ratio, or divide an amount by a ratio, with two or three parts.
Simplified ratio
Simplified ratio
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- As percentages of the total
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- As a fraction
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Solve a proportion
Find the missing value in A:B = C:D.
- D, the missing value
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Scale a ratio
Multiply both parts of a ratio by a scale factor.
- Scaled ratio
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Divide an amount by a ratio
Split a total into parts sized by a ratio, such as sharing a bill or a recipe.
- Divided amounts
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How it works
A ratio is a comparison of two or more quantities expressed as a:b, showing their relative sizes, and it can be simplified by dividing every part by their greatest common divisor.
- Enter the parts
Two parts, or three for A:B:C.
- Read the simplified ratio
Plus the percentage and fraction forms.
- Use the sections below
Solve a proportion, scale a ratio, or split an amount.
Simplifying, proportions and division
To simplify a ratio, divide every part by their greatest common divisor (GCD). For 24:36, the GCD is 12, so 24/12 : 36/12 gives 2:3. If A:B = C:D, then A × D = B × C, cross multiplication, which is how the missing value in a proportion is found.
Dividing an amount by a ratio
To split an amount X in ratio A:B, add the parts to get the total number of shares (A+B), then each part is X × A/(A+B) and X × B/(A+B). Splitting a $100 profit in ratio 2:3 gives $40 and $60.
Ratio versus fraction
A ratio compares two quantities directly: 2:3 means for every 2 of one thing there are 3 of another. A fraction such as 2/5 represents a part of a whole, here the share that the first quantity makes up of the total 5 parts. A ratio with a part of 0, such as 0:5, simplifies to 0:1; a ratio where every part is 0 has no meaningful simplification and is shown as is.
Frequently asked questions
How do you simplify a ratio?
Divide every part by their greatest common divisor (GCD). For 24:36, GCD(24, 36) = 12, so 24/12 : 36/12 = 2:3. The simplified ratio has the same proportional relationship as the original. The calculator performs this using the Euclidean algorithm, and also supports a third part for A:B:C ratios.
How do you solve a proportion where one value is unknown?
If A:B = C:D, then A × D = B × C, cross multiplication. Solving for D gives D = (B × C) / A. For 3:4 = 15:D, D = (4 × 15)/3 = 20. This is the foundation of proportional reasoning used in scaling recipes, maps, and similar triangles.
How do you divide an amount in a given ratio?
Sum the ratio parts, then allocate each part proportionally. To divide 100 in ratio 2:3, total parts = 5, Part A = 100 × (2/5) = 40, Part B = 100 × (3/5) = 60. For example, sharing a $100 profit between two partners in ratio 2:3 gives $40 and $60.
What is the difference between a ratio and a fraction?
A ratio compares two quantities, 2:3 means for every 2 of one there are 3 of another, while a fraction, 2/5, represents a part of a whole. The ratio 2:3 implies a total of 5 parts, with fraction 2/5 for the first quantity. Ratios can involve more than two parts, such as 1:2:3, unlike simple fractions.
What happens if a ratio part is zero?
A zero in a ratio, such as 0:5, means one quantity is absent. Simplifying 0:5 gives 0:1. A ratio where every part is zero, such as 0:0, is shown as 0:0 since there is nothing to divide by, and dividing an amount by a zero-sum ratio, such as parts 0 and 0, returns undefined for the same reason.