Ratio Calculator

Three things you can do with a ratio

A ratio such as 2 : 3 says how two amounts compare: for every 2 of the first there are 3 of the second. The calculator has three modes:

• Solve finds the missing value in a proportion A : B = C : D. Enter any three values and leave the fourth empty. Typical uses: scaling a recipe, reading a map scale, or converting at a fixed rate.
• Simplify reduces a ratio to the smallest whole numbers with the same proportion — 12 : 18 becomes 2 : 3 — and also works with decimals such as 1.5 : 2.25. It shows each term’s share of the total too.
• Scale resizes a ratio, either so the terms add up to a total (split $50 in the ratio 2 : 3) or so one term takes a new value (make A = 10 and scale B to match). An optional third term handles three-way splits.

Ratio and proportion formulas

Two ratios are in proportion when they have the same value: A ÷ B = C ÷ D. Multiplying both sides by B × D gives the cross-multiplication rule, from which any one term follows:

To simplify, clear any decimals by multiplying every term by the same power of ten, then divide every term by their greatest common divisor (GCD):

To share a total T in the ratio A : B : C, find the size of one part first:

A, B, C, D

the terms of the ratios; all must be greater than zero

g

the greatest common divisor of the (whole-number) terms

T

the total to be shared

Simplification is done with exact whole-number arithmetic, so a decimal ratio is never rounded on the way to its simplest form.

Worked examples

Solve 3 : 4 = C : 20. Cross-multiply the known diagonal pair: 3 × 20 = 60. Divide by the remaining term: 60 ÷ 4 = 15. Check: 3 ÷ 4 = 0.75 and 15 ÷ 20 = 0.75.

Simplify 1.5 : 2.25. The longest decimal has two places, so multiply both terms by 100: 150 : 225. The greatest common divisor of 150 and 225 is 75, and 150 ÷ 75 = 2, 225 ÷ 75 = 3, so the ratio is 2 : 3. The first term is 40% of the total and the second 60%.

Split 50 in the ratio 2 : 3. There are 2 + 3 = 5 parts, so one part is 50 ÷ 5 = 10. The shares are 2 × 10 = 20 and 3 × 10 = 30, which add back up to 50.

Things to watch

• Order matters. 2 : 3 and 3 : 2 are different ratios. Keep the terms in the same order on both sides of a proportion — boys to girls on the left means boys to girls on the right.
• Use the same units. A ratio of 50 cm to 2 m is 50 : 200 = 1 : 4, not 50 : 2.
• Ratios are not fractions of the whole. In 2 : 3 the first part is 2/5 of the total, not 2/3. The share lines in the Simplify result show this.
• Whole items don’t always divide evenly. Sharing 10 sweets in the ratio 1 : 2 gives 3⅓ and 6⅔; with indivisible items you have to round and accept a small difference.