Proportion Calculator – Rule of Three, Direct and Inverse
Enter three known values and find the fourth. Works for direct proportion (more → more) and inverse proportion (more → less), with the working shown.
For a direct proportion, if A gives B then C gives X = B × C ÷ A. Example: 4 kg cost 10, so 6 kg cost 10 × 6 ÷ 4 = 15. For an inverse proportion, X = A × B ÷ C: if 4 workers need 10 days, 6 workers need 4 × 10 ÷ 6 ≈ 6.67 days.
How to use the Proportion Calculator (Rule of Three)
- Choose Direct or Inverse proportion.
- Enter A and B (the pair you know) and C (the new value).
- X is calculated instantly, with the formula and numbers written out.
Direct proportion
Two quantities are directly proportional when they grow together at the same rate: double one and the other doubles. Price and weight, distance and fuel, ingredients and portions are typical examples. Cross-multiply: A/B = C/X, so X = B × C ÷ A.
Inverse proportion
Quantities are inversely proportional when one goes up as the other goes down, so their product stays the same. Workers and days, speed and travel time are classic examples: A × B = C × X, so X = A × B ÷ C.
Worked examples
| Problem | Type | Answer |
|---|---|---|
| A recipe for 4 uses 300 g flour. How much for 6? | Direct | 300 × 6 ÷ 4 = 450 g |
| 120 km uses 8 litres. How much for 300 km? | Direct | 8 × 300 ÷ 120 = 20 L |
| At 60 km/h a trip takes 3 h. How long at 90 km/h? | Inverse | 60 × 3 ÷ 90 = 2 h |
| 3 painters need 8 days. How long for 4? | Inverse | 3 × 8 ÷ 4 = 6 days |
Proportions and percentages
A percentage is a proportion with 100: if 45 is 100 %, what is 18? X = 100 × 18 ÷ 45 = 40 %. For percentage problems the percentage calculator is quicker.
Related tools: Percentage Calculator, Fraction Calculator and Average Calculator.
Frequently asked questions
What is the rule of three?
A method to find the fourth value of a proportion when you know three: X = B × C ÷ A for direct proportions.
What does directly proportional mean?
Two quantities change by the same factor: if one doubles, the other doubles too. Their ratio stays constant.
What does inversely proportional mean?
When one quantity doubles, the other halves. Their product stays constant.
How do I know if a problem is direct or inverse?
Ask: if the first value increases, does the second increase (direct) or decrease (inverse)? More kilos cost more (direct); more workers need fewer days (inverse).
What is cross multiplication?
Multiplying across the equals sign of A/B = C/X to get A × X = B × C, which gives X = B × C ÷ A.
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