Proportion & Ratio Solver
Solve a : b = c : d for the missing value by cross-multiplication — recipe scaling, map scales, mix ratios — with the scale factor and simplified ratios.
The missing value, the scale factor between the pairs, both sides as simplified ratios, and the ratio as a decimal and a percentage.
Example: 4 : 6 = 10 : d → d = 6 × 10 ÷ 4 = 15; scale factor 2.5; both sides simplify to 2 : 3 (66.67 %). Solve for a, b or c the same way.
Cross-multiply,
nothing more.
The one rule behind every proportion, and when it does not apply.
The rule
If a : b = c : d then a·d = b·c, so any one of the four follows from the other three: d = b·c ÷ a, c = a·d ÷ b, and so on. Scaling a recipe from 4 to 6 servings, reading a 1 : 50 000 map, mixing 2 : 1 epoxy or resizing a 1600 × 900 photo to 1200 wide are all the same line of arithmetic.
Scale and ratio
The scale factor c ÷ a is the multiplier that takes the left pair to the right pair. Each pair is also shown as a simplified ratio: whole numbers are divided by their greatest common divisor (4 : 6 → 2 : 3); with decimals the ratio is expressed as x : 1. The ratio value a ÷ b and the same as a percentage complete the picture.
Direct only
This is direct proportion — double one, double the other. Inverse proportion (twice the workers, half the time) multiplies instead: a·b = c·d. A quantity that is zero on the dividing side has no solution and is reported. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Cross-multiplication a·d = b·c; ratios simplified by the greatest common divisor when whole; direct proportion only
Last reviewed 21 September 2026. How results are checked: How we verify.