Rule of three calculator
If A corresponds to B, then C corresponds to B × C ÷ A. Example: if 4 people need 250 g of pasta, 6 people need 250 × 6 ÷ 4 = 375 g.
- Checked on thousands of cases
- Updated November 1, 2026
If corresponds to , then corresponds to:
Missing value
250 × 6 ÷ 4 = 375
Quick challenge
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Test yourself: every answer is computed by the tool, and the wrong choices are the most common traps.
How it works
Formula: x = B × C ÷ A
When two quantities are directly proportional (twice as many people, twice as much food), the missing value is found by cross-multiplication: x = B × C ÷ A. When they are inversely proportional (twice as many workers, half the time), multiply the two known values of the first situation and divide by the new one: x = A × B ÷ C. Check which case applies before calculating.
Worked examples
3 lb cost $12: how much for 5 lb?
12 × 5 ÷ 3 = $20.
A recipe for 4 people needs 300 g of flour: for 6?
300 × 6 ÷ 4 = 450 g.
4 people do a job in 6 days: and 3?
Fewer people, more time (inverse proportion): 4 × 6 ÷ 3 = 8 days.
Common mistakes
Multiplying the wrong numbers: 12 × 3 ÷ 5 = 7.2.
Multiply the two numbers across the diagonal (12 and 5), then divide by the third.
Using a direct rule of three for workers or speed: 4.5 days.
When one goes up and the other goes down, it is inverse: 8 days.
Mixing units (grams on one side, kilos on the other).
Convert everything to the same unit first.
If 100 corresponds to 15
| Value | Corresponds to |
|---|---|
| 10 | 1.5 |
| 20 | 3 |
| 25 | 3.75 |
| 50 | 7.5 |
| 75 | 11.25 |
| 120 | 18 |
| 150 | 22.5 |
| 200 | 30 |
| 250 | 37.5 |
| 500 | 75 |
| 1,000 | 150 |
Frequently asked questions
What is the rule of three?
A method to find a fourth value from three known ones when two quantities are proportional. If 3 kg cost 12, then 5 kg cost 12 × 5 ÷ 3 = 20.
When should I use the inverse rule of three?
When one quantity goes down as the other goes up. If 4 painters need 6 days, 3 painters need 4 × 6 ÷ 3 = 8 days.
How do I check my answer?
In a direct proportion, the ratio stays the same: B ÷ A should equal x ÷ C. In an inverse proportion, the product stays the same: A × B should equal C × x.