CornerTools

Ratio Calculator

Solve A:B = C:D for the missing value, simplify ratios, scale them, or split an amount in a ratio.

Fill in three of the four terms and leave the one to find empty.

In 3 : 4 = 9 : D

D = 12

3 : 4 = 9 : 12

Four ratio jobs on one page: find the missing term of a proportion, reduce a ratio to lowest terms, divide an amount in a ratio, and scale a ratio up or down. Terms can be whole numbers, decimals or fractions, the arithmetic is exact, and the working is shown with your own numbers.

How to use it

  • Solve — the proportion A : B = C : D with any one box left empty. It opens on 3 : 4 = 9 : D, which gives D = 12. A result that does not end as a decimal is also given as a fraction.
  • Simplify — a ratio of 2 to 6 terms separated by colons. Decimals and fractions are cleared first, so 1.5 : 2.25 becomes 2 : 3. A two-term ratio is also shown as 1 : n and n : 1.
  • Split — an amount divided in a ratio, with each share listed. Round to, beside the result, is Exact, 0.01 or 1.
  • Scale — a ratio multiplied through so that its terms add up to a Total, or so that its First term becomes a given value.

Terms cannot be negative, except in Solve, and a ratio needs at least one term above 0. Results with long decimals are shown to 10 significant figures and marked ≈. Everything runs in your browser.

How it works

A proportion says two ratios are equal, and in one the product of the outer terms equals the product of the inner terms. That gives the missing term by one multiplication and one division. The term divided by must not be 0 (“A can't be 0 when solving for D”).

To simplify, every term is multiplied by the lowest common denominator, which turns decimals and fractions into whole numbers, and then divided by the greatest common divisor of them all.

A split divides the amount by the sum of the terms to get one part, then multiplies each term by it. When rounding, each share is rounded down to the unit, and the units left over go one each to the shares that lost the most, the earlier share first on a tie. The shares therefore always add up to the amount: 100 in 1 : 1 : 1 at 0.01 gives 33.34 : 33.33 : 33.33. An amount that is not itself a multiple of the unit cannot be split that way, and the tool says so.

A : B = C : D means A × D = B × C
D = B × C ÷ A
Share = amount × term ÷ sum of the terms
Scale factor = new total ÷ sum of the terms, or new first term ÷ first term

Examples

Scaling a recipe

A recipe uses 2 cups of flour for 3 eggs. For 5 cups of flour, with Solve and 2 : 3 = 5 : D, the eggs needed are 7.5. As a fraction: 15/2.

  1. In a proportion, the two outer terms multiply to the same as the two inner terms. A × D = B × C
  2. Put in the numbers you have. D × 2 = 3 × 5 = 15
  3. Divide by 2. D = 15 ÷ 2 = 7.5

Splitting a profit in 2 : 3 : 5

With Split, an amount of 1,200 and the ratio 2 : 3 : 5, the three partners get 240 : 360 : 600.

  1. Add the terms of the ratio. 2 + 3 + 5 = 10
  2. Divide the amount by that total to find one part. 1,200 ÷ 10 = 120
  3. Multiply each term by one part. 2 × 120 = 240, 3 × 120 = 360, 5 × 120 = 600

A map scale

On a 1 : 50,000 map, 3.5 cm stands for D in 1 : 50,000 = 3.5 : D, which is 175,000 cm on the ground.

Mixing to a total

Cement, sand and gravel in 1 : 2 : 4, for 35 buckets in all: with Scale to a Total of 35, the mix is 5 : 10 : 20.

  1. Add the terms of the ratio. 1 + 2 + 4 = 7
  2. Divide the new total by that sum for the scale factor. 35 ÷ 7 = 5
  3. Multiply every term by the scale factor. 1 × 5 = 5, 2 × 5 = 10, 4 × 5 = 20

Frequently asked questions

A ratio compares parts with each other; a fraction compares one part with the whole. In a class with boys and girls in the ratio 2 : 3, the boys are 2 of every 5 pupils, which is the fraction 2/5, not 2/3.
Split 100 in the ratio. With Split, an amount of 100 and 2 : 3 : 5, the shares are 20 : 30 : 50, which are the percentages.
Yes. 2 : 3 and 3 : 2 are different ratios: the first term always goes with the first thing named.

See also