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Rule of Three Calculator

The Rule of Three Calculator solves proportion problems in seconds – both direct (more means more) and inverse (more means less). Enter three values and instantly get the missing fourth value, along with the formula and the calculation.

✓ Reviewed by Julian Bronski · updated June 2026

Your details

A (known) 3

01000000000+

equals B 12

01000000000+

C (given) 5

01000000000+

Result

Result X – direct (more means more)

–

Result X – inverse (more means less)

–

✓ Copied!

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How does the Rule of Three Calculator work?

The rule of three finds an unknown fourth value from three known ones. A and B are a matching value pair, C is the third value and X is the result.

Direct proportion (more means more)

Formula: X = B × C ÷ A. Example: 3 kg of apples cost €12. What do 5 kg cost? → 12 × 5 ÷ 3 = €20.

Inverse proportion (more means less)

Formula: X = A × B ÷ C. Example: 3 workers need 12 hours. How long do 5 workers need? → 3 × 12 ÷ 5 = 7.2 hours.

The calculator shows both results at once – simply pick the one that fits your problem.

Frequently asked questions

How does the rule of three work? ▾

The rule of three finds a fourth value from three known ones. You first reduce to a single unit, then scale up to the value you need. For direct proportion use X = B × C ÷ A; for inverse proportion use X = A × B ÷ C.

What is the difference between direct and inverse proportion? ▾

In direct proportion both quantities grow together: more quantity means more cost. In inverse proportion they move in opposite directions: more workers means less time. Rule of thumb: if twice as much also gives twice as much, it is direct proportion.

What is the rule of three formula? ▾

Direct: X = (B × C) ÷ A. Inverse: X = (A × B) ÷ C. Here A and B are the known value pair, C is the third value and X is the result you are looking for.

When do you use the rule of three in everyday life? ▾

For converting prices and unit costs, scaling recipes up or down, working with map scales, and comparing speeds or working times – wherever two quantities stay in a fixed ratio to each other.

How does the Rule of Three Calculator work?

Direct proportion (more means more)

Inverse proportion (more means less)

Frequently asked questions

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