How to use the calculator
- Choose direct or inverse proportion.
- Enter three of the four values and leave blank the one you want.
- Press Calculate.
Direct or inverse
- Direct: when one quantity goes up, the other goes up by the same factor. More pounds, higher price.
- Inverse: when one goes up, the other goes down. More workers, fewer days to finish.
direct: X = B × C ÷ A · inverse: X = A × B ÷ C
Direct: prices
3 lb of apples cost $12. How much do 5 lb cost?
X = 12 × 5 ÷ 3 = $20.
Inverse: work
4 people paint a house in 6 days. How many days for 3 people at the same pace?
X = 4 × 6 ÷ 3 = 8 days.
Percentages
What percentage of 180 is 45? If 180 is 100%, 45 is X: X = 45 × 100 ÷ 180 = 25%.
When it doesn't apply
The rule of three only works for proportional relationships. It won't work for a person's age and height, or for prices with bulk discounts. For percentage changes, the percentage increase calculator is quicker.
Frequently asked questions
How do I know if it's direct or inverse?
Ask what happens to the second quantity if you double the first. If it doubles too, it's direct; if it halves, it's inverse.
What is a compound rule of three?
One that links three or more quantities. You solve it as a chain of simple rules of three.