Proportion Calculator
Enter a pair of values that belong together (a ↔ b) and a new value c. The proportion calculator finds the matching x and shows the unitary method step by step.
Example: Type of proportion: direct – more of one means more of the other · Known value a 3 · corresponds to value b 4.5 · New value c 5 → Answer: x (goes with c): 7.5. Source: Department for Education – National curriculum in England: mathematics programmes of study, KS3 “solve problems involving direct and inverse proportion”. Updated: .
How it is calculated
What the calculator does
When two quantities are linked by a fixed rule, one known pair (a ↔ b) is enough to find the value x that goes with any new value c. In many countries this is called the rule of three; in English-speaking classrooms it is taught as direct and inverse proportion or the unitary method: find the value for one, then scale.
Direct proportion
Twice as much costs twice as much – the ratio b ÷ a stays the same. Formula: x = b ÷ a × c, the same as cross-multiplying a/b = c/x.
Example: 3 lb of apples cost $4.50. How much do 5 lb cost?
- 3 lb → $4.50
- 1 lb → $4.50 ÷ 3 = $1.50
- 5 lb → $1.50 × 5 = $7.50
Inverse proportion
Twice as many workers need half the time – the product a × b stays the same. Formula: x = a × b ÷ c.
Example: 4 workers take 6 days. How long do 3 workers take?
- 4 workers → 6 days
- 1 worker → 6 × 4 = 24 days
- 3 workers → 24 ÷ 3 = 8 days
Direct or inverse?
Ask: if a doubles, does b double (direct) or halve (inverse)? Typical direct proportions: quantity and price, hours and pay, distance and fuel used. Typical inverse proportions: number of workers and time taken, speed and journey time, number of people and share per person. If neither fits (for example age and height), proportion reasoning does not apply.
Percentages are direct proportions with 100% as the reference: 200 ↔ 100%, so 1% ↔ 2 and 15% ↔ 30. The percentage calculator handles these directly.
More calculators: percentages with the percentage calculator, exact ratios as fractions with the fraction calculator, and averages with the mean and standard deviation calculator.
Frequently asked questions
How do you solve a direct proportion problem?
Write down the known pair (3 lb → $4.50), divide to find the value for one (1 lb → $1.50), then multiply up to the value you need (5 lb → $7.50).
What is the difference between direct and inverse proportion?
In direct proportion both quantities grow at the same rate, so their ratio is constant. In inverse proportion one grows as the other shrinks, so their product is constant.
What is the formula for the rule of three?
Direct: x = b ÷ a × c (cross multiplication of a/b = c/x). Inverse: x = a × b ÷ c. Here b goes with a and x goes with c.
How do I use proportion to find a percentage?
Set the whole equal to 100%: 200 ↔ 100%, 2 ↔ 1%, 30 ↔ 15%. In the calculator: a = 100, b = 200, c = 15, direct – the answer is 30.
What is a compound proportion?
When more than two quantities are linked (for example workers, hours per day and days), solve it as a chain of simple proportions, changing one quantity at a time.
Sources and legal basis
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