Maths / Proportions
Rule of Three Calculator
Solve a rule of three, direct or inverse: if A gives B, what does C give? With the working shown, and a compound rule of three for several factors at once.
Rule of Three Calculator: In a direct rule of three, both quantities grow together, so x = B × C ÷ A: if 3 kg cost 12, 5 kg cost 20. In an inverse rule of three, one grows as the other shrinks, so x = A × B ÷ C: if 4 workers need 6 days, 3 workers need 8. The compound rule of three multiplies a known result by each factor's ratio, the right way up for direct and upside down for inverse factors. Runs 100% locally in your browser with zero server file uploads.
- Category
- School & study tools
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Runs entirely in your browser
x = (12 × 5) ÷ 3 = 20
Direct: if 3 gives 12, then 5 gives 20; both grow together.
Worked examples
Recipes: a cake for 4 needs 300 g of flour; for 6, 300 × 6 ÷ 4 = 450 g (direct). Speed: at 60 km/h a trip takes 3 hours; at 90 km/h, 60 × 3 ÷ 90 = 2 hours (inverse). Currency: if 5 euros buy 27 reais, 40 euros buy 27 × 40 ÷ 5 = 216 reais (direct).
For percentages directly, use the percentage calculator; for fractions, the fraction calculator.
A common mistake
Using a direct rule where the relation is inverse doubles the error instead of fixing it: with twice the workers, a job takes half the time, not twice. Before calculating, say aloud whether more of the first means more or less of the second.
How to use it
- Choose direct proportion (more gives more) or inverse (more gives less).
- Enter the three known values: A gives B, and C.
- Read x and the working; switch to Compound for problems with several factors.
Privacy & limitations
The calculation runs in your browser.
Related tools
Frequently asked questions
How do I know whether it is direct or inverse?
Ask whether more of one means more or less of the other. More kilograms cost more money: direct. More workers need fewer days for the same job: inverse.
Can I use it for percentages?
Yes: if 250 is 100%, what percentage is 60? A = 250, B = 100, C = 60 gives 24%.
What is the compound rule of three?
A problem with several factors, such as workers, hours a day, and days. Each factor is set as direct or inverse, and the known result is scaled by each in turn.
Free tool · runs in your browser · no account required