Rule of Three Calculator
Solve direct and inverse proportions step by step, with the arithmetic written out.
More of one means more of the other: kilos and price, kilometres and fuel.
x = 28
x = (12 × 7) ÷ 3
- 1. Multiply the diagonal pair: 12 × 7 = 84.
- 2. Divide by the remaining term: 84 ÷ 3 = 28.
What does this tool do?
Solves a proportion: if A corresponds to B, what corresponds to C? It does it for the two cases that exist and shows the arithmetic in two steps, so the answer can be checked by hand.
Direct or inverse
- Direct — more of one is more of the other. Three kilos cost 12, so seven kilos cost more.
Multiply across the known pair, divide by what is left:
x = (B × C) ÷ A. - Inverse — more of one is less of the other. Four machines take six hours, so eight machines
take fewer. The product of each pair is constant:
x = (A × B) ÷ C.
Choosing the wrong one does not produce an error, it produces a plausible number, which is why the page asks you to pick before it answers and explains what each one means.
Keep in mind
The tool refuses the two cases that have no answer — dividing by a zero first term in a direct
proportion, or a zero third term in an inverse one — and says which one it is instead of showing
Infinity. Everything runs in your browser.