Rule of Three Calculator
Solve a direct or inverse rule of three: if A corresponds to B, calculate what C corresponds to. Choose the type based on whether the two quantities grow together (direct) or one grows while the other shrinks (inverse).
How is it calculated?
Direct (more A, more B): if A corresponds to B and C corresponds to X, then X = (B × C) ÷ A — more C means more X. Inverse (more A, less B): X = (A × B) ÷ C — more C means less X. The difference between the two isn't in the numbers, but in whether the two quantities move in the same direction or opposite directions.
Examples
Direct: if 3 kg cost 90, how much do 7 kg cost?
7 kg costs 210.
Inverse: 4 workers take 6 days, how long do 8 take?
8 workers take 3 days.
Direct and inverse, in the same table
The steps are the same for both: lay out what you already know (A corresponds to B) and what you're looking for (C corresponds to X), decide the type with the question "if I increase one, does the other increase or decrease?", and apply the matching formula.
| Type | When it's used | Formula |
|---|---|---|
| Direct | As one quantity increases, the other increases in the same proportion | X = (B × C) ÷ A |
| Inverse | As one quantity increases, the other decreases in the same proportion | X = (A × B) ÷ C |
Common use cases
Direct: prices and quantities, recipes, map scales, unit conversion. Inverse: splitting work among more or fewer people, speed and time over a fixed distance, or any case where dividing among more parts reduces each part's share.
A percentage is a special case of the direct rule of three with a base of 100 — to work only with percentages, the percentage calculator is more direct; for percentage changes between two values, the percentage increase calculator.