Calcwise / Maths and units / Rule of three calculator
Rule of three calculator
If A corresponds to B, what corresponds to C? Choose the type of proportion and fill in three numbers.
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About this tool: Rule of three calculator
The rule of three finds a fourth number from three known ones. It is how you scale a recipe, convert a price for another quantity or work out how long a job takes with more people.
In a direct proportion both quantities grow together, such as price and weight. In an inverse proportion one grows as the other shrinks, such as workers and days needed to finish the same job.
Formula
Direct: A is to B as C is to X, so X = B × C ÷ A. Inverse: A × B = C × X, so X = A × B ÷ C.
Worked example
Direct: 4 kg cost 10, so 6 kg cost 10 × 6 ÷ 4 = 15. Inverse: 4 workers need 10 days, so 6 workers need 4 × 10 ÷ 6 = 6.67 days.
Sources and data
- Formulas and data last reviewed
- Accuracy
- The result is plain maths: with valid input it is exact, and we only round to cents.
Frequently asked questions
How do I know if a proportion is direct or inverse?
If doubling one number doubles the other (price and amount), it is direct. If doubling one halves the other (workers and days), it is inverse.
Can any value be zero?
A is the divisor in a direct proportion and C in an inverse one, so those cannot be zero.
Is the result exact?
The calculation is exact. The display shows up to 6 decimal places.