Solve proportional and inverse rule-of-three problems: if A corresponds to B, what does C correspond to?
How to use the Rule of Three
Enter the known pair: A corresponds to B.
Enter C, the value you want to scale.
Choose proportional or inverse and read the result.
A rule of three (Dreisatz) calculator for proportional and inverse relationships, one of the most useful everyday maths tricks and a staple of school exercises. The rule of three finds an unknown value from a known ratio.
In the proportional case, if A corresponds to B, then C corresponds to B times C divided by A, because the two quantities rise and fall together.
The inverse case is for quantities that move in opposite directions: as one goes up, the other goes down. Here, if A corresponds to B, then C corresponds to A times B divided by C, for example more workers meaning less time for a job.
Enter the known pair and the value you want to scale, choose whether the relationship is proportional or inverse, and the answer appears instantly with the calculation laid out.
Uses are everywhere: scaling a recipe up or down, working out a unit price, converting a rate, or estimating how long a task takes with more or fewer people. All four values and the result can be decimals, so it works for prices, quantities, speeds and time. Everything runs in your browser.
Frequently asked questions
A method to find an unknown value from a known ratio. If A corresponds to B, then C corresponds to B times C divided by A (proportional).
When the quantities move in opposite directions: as one goes up, the other goes down. For example, more workers means less time, so the result is A times B divided by C.
Yes. All four values and the result can be decimals, so it works for prices, quantities, speeds and time.
If 3 apples cost 1.50, then 5 apples cost 1.50 times 5 divided by 3, which is 2.50. The price scales in proportion to the quantity.
If 4 workers finish a job in 6 hours, then 3 workers take 4 times 6 divided by 3, which is 8 hours. Fewer workers means more time, the inverse relationship.
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