Rule of three calculator: direct and inverse proportion

Use three known values in a proportion to solve for the fourth. Choose direct proportion when both quantities rise or fall together, and inverse proportion when one rises as the other falls. The result assumes a constant proportional relationship.

Solve a proportion

How to choose direct or inverse proportion

Ask what happens to the second quantity when the first changes, while the other conditions stay the same. If both move in the same direction, the relationship is direct; if one increases while the other decreases, it is inverse. A real-world relationship may not be proportional when other factors change.

Worked examples

• Direct — 3 kg cost R$27. At the same unit price, 5 kg cost 27 × 5 ÷ 3 = R$45.
• Inverse — at 80 km/h, a fixed journey takes 3 hours. At 120 km/h, under the same conditions, the estimate is 80 × 3 ÷ 120 = 2 hours.
• Recipe scaling — if a recipe uses 300 g of flour for 8 servings, 12 servings use 300 × 12 ÷ 8 = 450 g.

When this method is not enough

The rule of three assumes the quantities have a stable proportional relationship. It does not account for fixed fees, tiered prices, waste, changing speed or other conditions. For a trip, for example, the inverse estimate assumes the same route and no stops or traffic changes.

Frequently asked questions