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Rule of Three Calculator

Enter three known values and get the missing fourth one. Choose Inverse when one quantity goes down as the other goes up.

Type of proportion

Both grow together: more kilos cost more, more people need more food.

X7.5

If 3 is 4.5, then 5 is 7.5

X = B × C ÷ A = 4.5 × 5 ÷ 3 = 7.5

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How it works

The rule of three solves the proportion A is to B as C is to X. Which formula applies depends on how the two quantities are related:

Type When to use it Formula
Direct Both quantities rise and fall together X = B × C ÷ A
Inverse One rises when the other falls X = A × B ÷ C

In a direct proportion the ratio stays the same: B ÷ A = X ÷ C. In an inverse one, the product stays the same: A × B = C × X. The calculator multiplies before dividing so that whole-number results come out exact, and it shows up to six decimals.

Examples of direct proportion

  • Shopping. 3 kg of apples cost $4.50. How much do 5 kg cost? 4.50 × 5 ÷ 3 = $7.50.
  • Recipes. A recipe for 4 people uses 300 g of rice. For 6 people: 300 × 6 ÷ 4 = 450 g.
  • Map scale. On a map, 1 cm is 250 m. A route of 4.2 cm is 250 × 4.2 ÷ 1 = 1,050 m.
  • Percentages. 45 out of 60 questions right: 100 × 45 ÷ 60 = 75%.

Examples of inverse proportion

  • Work and time. 4 workers need 6 days to paint a building. 8 workers need 4 × 6 ÷ 8 = 3 days.
  • Speed and time. At 60 mph a trip takes 2 hours. At 80 mph it takes 60 × 2 ÷ 80 = 1.5 hours.
  • Sharing supplies. Food for 10 people lasts 12 days. For 15 people it lasts 10 × 12 ÷ 15 = 8 days.

Common mistakes

  1. Using direct when it should be inverse. If the answer seems absurd (8 workers taking 12 days), switch the type.
  2. Mixing units. Keep A and C in the same unit, and B and X in the same unit. Convert minutes to hours or grams to kilograms first.
  3. Applying it to things that are not proportional. Taxi fares with a fixed starting fee, or bulk discounts, do not grow in proportion, so the rule of three gives the wrong answer for them.

Frequently asked questions

What is the rule of three?

A quick way to find a missing value when two quantities are proportional. If you know that A corresponds to B, the rule of three tells you what corresponds to a third value C. For example, if 3 kg cost $4.50, then 5 kg cost 4.50 × 5 ÷ 3 = $7.50.

How do I know if a proportion is direct or inverse?

Ask what happens when the first quantity doubles. If the second one doubles too (more kilos, higher price), it is direct. If the second one halves (twice the workers, half the days), it is inverse.

Can I calculate a percentage with the rule of three?

Yes. To find what percentage 45 is of 60, enter 60 → 100 and 45 as C; the result is 75, so 45 is 75% of 60. The percentage calculator does the same in one step.

Why does it say I cannot divide by zero?

In a direct proportion the formula divides by A, and in an inverse one by C. If that value is 0, there is no proportion to work with, so change it to a number other than zero.

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