Math
Proportion Calculator
Solve any direct or inverse proportion in seconds
This proportion calculator solves the rule of three: if A goes with B, what goes with C? Choose whether the proportion is direct or inverse and we give you the answer with the setup.
The key idea
A proportion is not a formula: it is asking how things change together
Before you multiply, decide whether one quantity goes up or down when the other goes up. If 3 lb cost $6, 7 lb cost $14 (direct). If 4 painters take 6 days, 3 painters take 8 (inverse). Picking the wrong type gives an answer that makes no sense.
How it is calculated
- Direct
- When one quantity goes up, the other goes up in the same ratio (more pounds, higher price).
- Inverse
- When one goes up, the other goes down (more workers, fewer days).
A → B, C → X ⇒ X = A × B / C
Worked example
Direct: 3 lb of apples cost $6. How much do 7 lb cost? X = 6 × 7 / 3 = $14.
Inverse: 4 painters take 6 days. How long do 3 take? X = 4 × 6 / 3 = 8 days.
Common questions
Frequently asked questions
How do I know if a proportion is direct or inverse?
Double one quantity and see what happens to the other: if it also doubles, it is direct; if it halves, it is inverse.
What is the formula for a direct proportion?
X = B × C / A: multiply the two values that cross with the unknown and divide by the one left over. If 3 lb cost $6, 7 lb cost 6 × 7 / 3 = $14.
What is the formula for an inverse proportion?
X = A × B / C: multiply the two values of the first pair and divide by the third. If 4 painters take 6 days, 3 painters take 4 × 6 / 3 = 8 days.
What is the rule of three?
It is the method of finding the fourth value of a proportion when you know the other three. It is the same as cross-multiplying A / B = C / X and solving for X.
Does it work for percentages?
Yes: if 200 is 100%, then 50 is X%, and X = 50 × 100 / 200 = 25%. You can also use the percentage calculator.
When does a proportion not work?
When the quantities are not proportional, for example a price with a fixed fee or a taxi with a base fare. The fixed part does not grow with the quantity, so the proportion breaks.
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