Rule of Three Calculator - Cross-Multiplication Online
Proportion type
A is to B as C is to X (if A goes up, X goes up).
Result X
Value of X
Formula: X = (B × C) ÷ A
How to use this calculator?
1. Choose direct or inverse proportion.
2. Enter the two known values A and B that go together.
3. Enter the third value C, the one you want to match.
4. Read X and the detailed formula, updated as you type. Decimal commas are accepted.
Quick answer
How do you do the rule of three?
If A corresponds to B, then C corresponds to X = (B × C) ÷ A, which is cross-multiplication. Example: if 3 kg cost €12, then 5 kg cost (12 × 5) ÷ 3 = €20. For inverse proportion, X = (A × B) ÷ C: if 4 people take 6 days, 3 people take (4 × 6) ÷ 3 = 8 days.
| Situation | Formula | Result |
|---|---|---|
| 3 kg = €12, 5 kg = ? | (12 × 5) ÷ 3 | €20 |
| 100 km = 6 l, 250 km = ? | (6 × 250) ÷ 100 | 15 l |
| 4 people = 6 days, 3 people = ? | (4 × 6) ÷ 3 | 8 days |
About the Rule of three
What is it?
The rule of three, or cross-multiplication, finds a fourth value from three known values when two quantities are proportional. It is handy for scaling a recipe, working out a unit price, converting a map scale or a percentage.
Why use it?
Cross-multiplication is simple in theory, but it is easy to swap two values, especially with decimals. This calculator shows the result and the formula filled in with your own numbers, so you can check the reasoning. It also handles inverse proportion, a frequent source of mistakes.
How does it work?
For a direct proportion, if A matches B, then C matches X = (B × C) ÷ A. Example: a recipe for 4 people needs 250 g of flour; for 6 people, X = 250 × 6 ÷ 4 = 375 g. For an inverse proportion, X = (A × B) ÷ C: if 3 workers need 8 days for a job, 4 workers need 3 × 8 ÷ 4 = 6 days, assuming they work at the same pace.
Usage tips
- Keep values that belong together on the same row (4 people and 250 g).
- Check that the quantities really are proportional: flat fees and tiered prices are not.
- Use inverse proportion for speed and travel time, or team size and working time.
- Use the same unit for A and C (all grams or all kilograms, for example).
- For a unit price, enter the quantity as A, the price as B and the new quantity as C.
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