Ratio Calculator

1. Enter the two numbers of your ratio as A and B.
2. Read the simplified ratio and its decimal form, updating as you type.
3. To scale, enter a third number C and the calculator solves A : B = C : D for the missing value.

Each output serves a different purpose:

A ratio compares two quantities, telling you how much of one there is for a given amount of another. Written with a colon, 2:3 means two units of the first for every three of the second. Ratios describe recipes, maps, mixtures, odds and screen shapes, anywhere a relationship between two amounts matters more than the amounts themselves.

Because a ratio is a comparison, you can multiply or divide both sides by the same number without changing it: 8:12 and 2:3 describe exactly the same relationship. Reducing to the smallest whole numbers is what makes ratios easy to read and compare.

To simplify, it divides both numbers by their greatest common divisor. To scale, it uses cross-multiplication to keep the proportion equal.

The reduced ratio is A/gcd : B/gcd, and a proportion is solved by cross-multiplying, since A/B = C/D => D = (B * C) / A.

1. Find the greatest common divisor of A and B.
2. Divide both by it to get the simplest ratio.
3. To scale, cross-multiply to find the value that keeps the proportion.

The decimal form, simply A divided by B, gives a single number for quick comparisons.

Simplify 8 : 12. The greatest common divisor of 8 and 12 is 4, so 8/4 : 12/4 = 2:3. As a decimal, 8 divided by 12 is about 0.667.

Now scale it: if 3 : 4 and you want the value paired with 9, cross-multiply to get D = (4 * 9) / 3 = 12, so 3 : 4 = 9 : 12. This is exactly how a recipe for four is scaled up for a larger group.

Ratios that share no common factor, such as 5 : 7, are already in lowest terms and cannot be reduced further.

These three ways of comparing amounts are closely related, and switching between them is often useful.

Note the shift: a 1 : 4 ratio is 1 out of 5 as a fraction, because the parts total five. To turn any of these into a percentage, the percentage calculator does it in a step.

A ratio depends only on the two numbers and the factor they share, and a few patterns are worth knowing.

Shared Factors

The larger the common factor, the more a ratio reduces; numbers that share no factor are already simplest.

Order of the Numbers

A ratio is directional: 3 : 4 is not the same as 4 : 3, so the order of A and B matters.

Scaling Both Sides

Multiplying or dividing both numbers by the same value changes the figures but not the ratio itself.

Decimals in the Inputs

The simplified whole-number ratio rounds each side to an integer first, while the decimal form uses your exact values.

Scaling Recipes and Mixtures

Keep the same proportions when cooking for more people or mixing paint, fuel or fertiliser.

Reading Maps and Models

A map scale is a ratio, so solving a proportion turns a map distance into a real one.

Comparing and Sharing

Split a sum or a workload in a given ratio, or compare two ratios by their decimal form.

1. Reversing the Order

A : B and B : A are different ratios. Keep the quantities in the order they belong.

2. Confusing Ratio with Fraction

A 1 : 4 ratio is 1 out of 5 as a fraction, not 1 out of 4. The parts add up.

3. Adding to Both Sides

You scale a ratio by multiplying or dividing both sides, never by adding the same number.

4. Not Simplifying Fully

Divide by the greatest common divisor, not just any common factor, to reach lowest terms.

5. Cross-multiplying the Wrong Pair

In A : B = C : D, the missing D equals B times C divided by A. Line the terms up carefully.

The simplification is exact for whole numbers, and the proportion is solved precisely, but it describes only two quantities.

Divide both numbers by their greatest common divisor. For 8 : 12 the GCD is 4, giving 2 : 3. This calculator reduces any ratio to its lowest terms.

Cross-multiply. If A : B = C : D and D is missing, then D = B x C / A. Enter A, B and C here and the missing value appears.

A ratio compares two quantities, written with a colon such as 2 : 3, meaning two of the first for every three of the second. It shows a relationship rather than totals.

A 1 : 4 ratio compares one part to four other parts, which is 1 out of 5 as a fraction, because the parts add to five. They are related but not the same.

Yes. A : B is not the same as B : A. A ratio of 3 : 4 describes a different relationship from 4 : 3.

Set up a proportion. If a recipe for 4 needs a 3 : 4 ratio and you cook for 9, solve 3 : 4 = 9 : D to get the scaled amount.

Yes. Divide the first number by the second. The ratio 2 : 3 is about 0.667 as a decimal, which makes two ratios easy to compare.

It is the ratio reduced so the two numbers share no common factor other than one, such as 2 : 3 rather than 8 : 12.

No. The calculation runs in your browser, and nothing you enter is sent anywhere unless you Save a result, which stays on this device only.

• Ratio (Wikipedia).
• Ratios (Maths Is Fun).
• Proportions (Maths Is Fun).