Ratio Calculator

About the Ratio Calculator

This ratio calculator combines three tools on one page. ① Solve a proportion finds the missing term when you leave any one of the four boxes empty. ② Split by ratio divides a total — prize money, shared costs, ownership — in a given ratio. ③ Simplify a ratio turns ratios such as 12:18:30, 0.5:1.25 or 1/2:1/3 into the simplest ratio of whole numbers.

Use it to scale recipes, work with map scales, divide shares or check math homework.

How to use

1. In ①, leave empty the one box of a : b = c : d you want to find. The value of x and the working appear immediately.
2. In ②, enter the total and the ratio (e.g. 2:3:5) to see each share in a table. Tick Whole numbers only to split into whole units, such as whole dollars or items.
3. In ③, type a ratio to reduce it to its simplest whole-number form.

Solving proportions with cross-multiplication

In a : b = c : d, the outer terms (a and d) are the extremes and the inner terms (b and c) are the means. In every true proportion, a × d = b × c.

Example: 2 : 3 = 10 : x → 2 × x = 3 × 10 → x = 15. If a recipe for 2 people needs 30 g of sugar, 5 people need 2 : 30 = 5 : x → x = 75 g.

How to split an amount by ratio

Each share = total × (its part ÷ sum of the parts). Splitting $1,000 in the ratio 2 : 3 : 5 gives a sum of parts of 10, so the shares are $200, $300 and $500.

When the amount doesn’t divide evenly — like $100 split 1 : 1 : 1 — tick Whole numbers only. Each share is rounded down, then the leftover units go one by one to the shares with the largest remainders (largest remainder method), so you get $34, $33 and $33 and the total still matches.

How to simplify a ratio

• Whole numbers: divide every term by the greatest common factor. 12 : 18 : 30 → ÷6 → 2 : 3 : 5
• Decimals: multiply by 10, 100… to get whole numbers, then divide. 0.5 : 1.25 → ×100 → 50 : 125 → ÷25 → 2 : 5
• Fractions: multiply by the least common multiple of the denominators. 1/2 : 1/3 → ×6 → 3 : 2