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Proportion (Solve a/b = c/d)

Also known as cross multiplication · solve a proportion · find x in a proportion · ratio and proportion · a is to b as c is to d · cross multiply and divide · equivalent fractions solver

ab=cd\frac{a}{b} = \frac{c}{d}

Units aren’t used in this calculation — every value is a plain number.

Worked example: 3/4 = c/20 → c = 15 — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value.

See also
Percent of a Number — the special case where one of the two ratios is something-per-hundredRecipe Scaling (Ingredient for a New Yield) — a proportion with the four slots already named: quantity to servingsUnit Price (Price per Unit Quantity) — what the same ratio is called once one side is fixed at a single unit

Learning zone

Two ratios are equal, three of the four numbers are known, and cross-multiplication finds the fourth. Multiply the two terms that face each other diagonally, divide by the one that faces the blank. It is the most reused piece of arithmetic in any trade: a scale drawing, a map distance, a mix ratio, a gear train, a currency conversion, a dilution, a recipe for a different number of people.

The mechanics are just algebra. a/b=c/da/b = c/d multiplied through by bdbd gives ad=bcad = bc, and dividing that by whichever term you do not want leaves the one you do. Nothing in the derivation cares what the numbers mean, which is exactly where the danger sits.

What the arithmetic cannot check for you is orientation. Both ratios have to be read the same way round — kilometres over centimetres on the left demands kilometres over centimetres on the right, never centimetres over kilometres — and if you flip one of them the equation still solves, still returns a confident number, and is wrong by the square of the scale factor. The reliable defence is to write the units into the fraction and see whether the ones you do not want cancel. If a map scale of 1 cm to 2.5 km is set against a measured 6 cm, the arrangement 1/2.5=6/d1/2.5 = 6/d gives d=15d = 15 km, and the units read cm-per-km on both sides. Flip one side and you get 2.4, which is a real number and the wrong answer.

Proportion (Solve a/b = c/d)
ab=cd\frac{a}{b} = \frac{c}{d}
Where
  • aa= First term
  • bb= Second term
  • cc= Third term
  • dd= Fourth term
Missing one of these? Work it out first, then come back