Ratio calculator and simplifier

Four ratio jobs, four tabs

• Solve A : B = C : D — leave one box empty to find the missing term by cross-multiplication.
• Simplify — reduce any ratio, with any number of terms, to its lowest whole-number form.
• Scale — you know one term of an equivalent ratio and want all the others.
• Split a total — divide an amount between people or parts in proportion.

Solving a proportion

Two ratios are equal when their cross products match: A : B = C : D means A × D = B × C. Rearranging that single identity gives every missing term:

If you fill in all four boxes the tool switches to checking mode and tells you whether the two ratios are actually equivalent.

Simplifying a ratio

Divide every term by the greatest common divisor of all of them. 1920 : 1080 share a GCD of 120, giving 16 : 9. Decimal terms are scaled up by a power of ten first, so 2.5 : 1.5 becomes 25 : 15 and then 5 : 3. The tool also reports the “1 : n” normalised form, which is how aspect ratios and gear ratios are usually quoted.

Splitting a total

To share 1,200 in the ratio 2 : 3 : 5, add the terms to get 10 shares, divide 1,200 by 10 to get 120 per share, then multiply: 240, 360 and 600. The split tab shows the exact value and a rounded value for each part, plus its percentage of the total, so you can see immediately if rounding has left a penny unallocated.

Common ratios you may be looking for

Ratios, fractions and percentages

A two-term ratio A : B and the fraction A/B carry the same information but answer different questions. The ratio compares two parts to each other; the fraction compares one part to the other. If a class is 3 : 2 boys to girls, then boys are 3/5 of the class — 60% — and 3/2 as many as the girls. Confusing “part to part” with “part to whole” is the classic ratio mistake, so the simplify tab always shows each term as a percentage of the total as well.

Scaling recipes and drawings

Scaling keeps a ratio equivalent by multiplying every term by the same factor. If a recipe for four people uses 300 g of flour and you are cooking for six, the factor is 6 ÷ 4 = 1.5, so every ingredient is multiplied by 1.5. Map and model scales work identically: a 1 : 50 drawing means 1 cm on paper is 50 cm in reality, so a 7.4 cm line represents 370 cm.

Accuracy

Simplification uses exact integer arithmetic with arbitrary-precision greatest common divisors, so large terms reduce correctly. Proportion solving and splitting use double-precision arithmetic and display up to ten decimal places. Everything runs locally in your browser; no numbers are uploaded.