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Math

Ratio Calculator

Simplify a ratio, solve a proportion A : B = C : D for the missing value, or split a total in a given ratio, with short step-by-step working.

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Simplify a ratio A : B
Whole numbers or decimals, for example 1.5 : 2.5.
Solve a proportion A : B = C : D
Fill in three values and leave the one you want to find empty.
Split a total in the ratio A : B

How to use the calculator

The page has three separate calculators.

  • Simplify a ratio: enter A and B and press Simplify. Decimals are allowed, for example 1.5 : 2.5.
  • Solve a proportion: fill in three of the four boxes in A : B = C : D and leave the unknown one empty. Press Solve to find it.
  • Split a total: enter an amount and the ratio A : B to see how much each side gets.

Each result comes with the short working, so you can follow or check it.

How it works

Simplifying

A ratio is in simplest form when both terms are whole numbers with no common factor other than 1. If a term has decimals, both terms are first multiplied by the same power of 10 to remove them. Then both are divided by their greatest common factor.

Example: 1.5 : 2.5 becomes 15 : 25 after multiplying by 10. The greatest common factor of 15 and 25 is 5, so the simplest form is 3 : 5.

Solving a proportion

Two equal ratios A : B = C : D satisfy A × D = B × C (cross-multiplication). Solve this for the missing value.

Example: 2 : 4 = 6 : D gives D = 4 × 6 ÷ 2 = 12.

Splitting a total

Add the ratio terms to get the number of equal parts, divide the total by that number to get one part, then multiply.

Example: split 100 in the ratio 2 : 3. There are 2 + 3 = 5 parts, one part is 100 ÷ 5 = 20, so the shares are 2 × 20 = 40 and 3 × 20 = 60.

Good to know

  • The second term of a ratio (B, and D in a proportion) cannot be zero.
  • The order matters: 2 : 3 is not the same as 3 : 2.
  • Ratios are handy for recipes, mixing paint or concrete, map scales, screen aspect ratios and sharing costs.
  • Simplifying uses exact arithmetic on the digits you typed, so 0.1 : 0.3 becomes exactly 1 : 3. Up to 10 decimal places are accepted.
  • Results of proportions and splits are rounded to at most 10 decimal places for display.

Frequently asked questions

How do I simplify a ratio with decimals?

Multiply both terms by 10, 100 or 1000 until neither has decimals, then divide both by their greatest common factor. For 0.25 : 2, multiplying by 100 gives 25 : 200, and dividing by 25 gives 1 : 8. The calculator does both steps for you.

What does it mean to solve a proportion?

A proportion says that two ratios are equal, such as 3 : 4 = 9 : x. Solving it means finding the missing value that makes the statement true. Cross-multiplying gives 3x = 36, so x = 12.

How do I divide money in a ratio?

Use the split section. Enter the amount and the ratio. The calculator adds the ratio terms, works out the value of one part and multiplies it by each term. For 900 in the ratio 1 : 2 the shares are 300 and 600.

Why can't B be zero?

A ratio A : B compares A with B, which means dividing A by B. Division by zero is undefined, so a ratio whose second term is zero has no meaningful value.