Rule of Three Calculator
Find the missing value in a proportion. If A goes with B, enter C to find what goes with it, for direct proportions (more → more) or inverse ones (more → less).
x =
20
If 3 → 12, then 5 → 20
Check the highlighted fields to see your result.
Results are estimates for information only and do not constitute financial, medical, or legal advice.
How the rule of three works
In a direct proportion, both values change in the same direction: twice the weight costs twice as much. In an inverse proportion they change in opposite directions: twice as many people finish a job in half the time.
The formulas
Direct: x = B × C ÷ A
Inverse: x = A × B ÷ C
Worked example
- Direct: 3 kg of apples cost 12. How much do 5 kg cost? x = 12 × 5 ÷ 3 = 20.
- Inverse: 4 people paint a house in 6 days. How long do 3 people take? x = 4 × 6 ÷ 3 = 8 days.
Frequently asked questions
How do I know if it is direct or inverse?
Ask yourself what happens to one value when the other grows. If both grow together (more kilos, more money), it is direct. If one grows while the other shrinks (more workers, fewer days), it is inverse.
Is the rule of three the same as cross multiplication?
Yes, for direct proportions. Writing A/B = C/x and cross-multiplying gives x = B × C ÷ A, which is exactly what the calculator does.
Can I use decimals or negative numbers?
Yes. Only the value you divide by can’t be 0: A in a direct proportion and C in an inverse one.