Rule of three calculator
If 3 cost 12, what do 7 cost? That is the rule of three: a/b = c/d, solved for d. Inverse proportion has its own mode, because applying the direct rule to it — more workers, less time — is the classic mistake.
- Constant of proportion
- 4.0000
- Equation solved
- 3 / 12 = 7 / d
- Value per unit
- 4.0000
- Answer with the other rule
- 5.1429
- c as a percentage of a
- 233.33 %
The formula
Direct: a/b = c/d, so d = b × c / a. Inverse: a × b = c × d, so d = a × b / c. The constant of proportion is b/a in the direct case and a × b in the inverse case.
Worked example
If 3 items cost 12, then 7 cost 12 × 7 / 3 = 28. Inversely, if 4 workers take 6 days, 3 workers take 4 × 6 / 3 = 8 days — and the direct rule would wrongly have said 4.5.
How to use it
- 1Ask whether doubling one quantity doubles or halves the other. Doubling the price doubles the cost: direct. Doubling the speed halves the time: inverse.
- 2Keep the units matched: a and c in the same unit, b and d in the same unit.
- 3The answer under the other rule is shown so you can see how far wrong the wrong choice would be.
Questions people ask
Why is it called the rule of three?
Because three values are known and the fourth is found. In French and Spanish teaching it is the standard name; in English it is more often called cross-multiplication or solving a proportion.
When does the rule of three not apply?
When the relationship is not proportional — a fixed fee plus a rate, a bulk discount, or anything with a threshold. Those need the actual formula, not a ratio.
Last reviewed: 2026-10-20