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Rule of three calculator

The rule of three works when two quantities change together and you know three of the four values.

Choose direct or inverse, fill in A, B and C, and the calculator gives you X.

How it's calculated

Direct: X = B × C ÷ A. Use it when both quantities grow together (more kilos, higher price).
Inverse: X = A × B ÷ C. Use it when one grows and the other shrinks (more people, fewer days).

An example

If 3 kilos cost $1,000, 5 kilos cost $1,666.67.

If 4 people paint a house in 12 days, 6 people paint it in 8 days.

Frequently asked questions

How do I know if it is direct or inverse?

If one quantity goes up when the other goes up, it is direct. If one goes down when the other goes up, it is inverse.

How do I work out a direct proportion by hand?

Cross multiply the two known values on the diagonal and divide by the one left. If 3 is to 600, 5 is to 600 × 5 ÷ 3 = 1,000.

Can I use it for percentages?

Yes. If 200 is 100%, 50 is 25%: that is a direct proportion with A = 200, B = 100 and C = 50.

Key terms

Direct proportion: Both quantities go up or down together.
Inverse proportion: One quantity goes up when the other goes down.

The same calculation in other countries

Up-to-date official data

We check the official sources automatically, every day.

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