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Rule of three calculator

Solve a simple rule of three (direct or inverse): enter three values and find the fourth.

X (result)
25
Proportion2 / 10 = 5 / X
Guide How to use the rule of three Interactive lesson: The half nobody teaches 3 painters take 12 days. And 4 painters? If you answered 16, you fell for the inverse-proportion trap.

How the calculation works

The rule of three finds an unknown value from a proportion between two quantities. The key is first deciding whether they are directly or inversely proportional.

Direct rule of three

When one quantity grows, the other grows in proportion (more kilos → more price). Set up the proportion and cross-multiply:

A/B = C/X → X = (B × C) / A

Example: if 2 kg cost R$10, how much for 5 kg? X = (10 × 5) ÷ 2 = R$25.

Inverse rule of three

When one grows, the other shrinks (more workers → less time). Here the products are equal:

A × B = C × X → X = (A × B) / C

Example: if 4 workers take 12 days, how long for 6? X = (4 × 12) ÷ 6 = 8 days.

How to tell which to use

Ask: "if I double the first quantity, does the second double or halve?" Double → direct; halve → inverse.

Examples

  • If 2 kg cost R$10, how much for 5 kg? Direct → X = (10×5)/2 = R$25.
  • If 4 taps fill the tank in 6 h, how long for 3? Inverse → X = (4×6)/3 = 8 h.

Frequently asked questions

When to use the inverse rule of three?

When increasing one quantity decreases the other — e.g., more workers, less time to finish.

What is cross-multiplying?

In the direct rule A/B = C/X, you multiply the diagonal terms (A×X = B×C) and isolate X. It is just solving the proportion.

What about three or more quantities?

That is the compound rule of three: analyze each quantity against the unknown separately. We have a dedicated calculator.

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Updated on June 17, 2026 · by Rafael Rossi · Methodology & sources