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Rule of Three Calculator

The rule of three finds an unknown value from three known ones that are in proportion. Enter A, B and C — "A is to B as C is to X" — and it solves X, in direct or inverse proportion.

Your numbers

Direct: more hours, more output. Inverse: more workers, less time.

A is to B...

...as C is to X.

The known value of the other pair.

Result

Value of X
10
Proportion
Directly proportional
Step by step
StepDetail
Setup3 is to 6 as 5 is to X
TypeDirectly proportional
FormulaX = (6 x 5) / 3
ResultX = 10
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Direct rule of three

Set it up as A is to B as C is to X. In direct proportion you cross multiply: X = (B x C) / A. Example: if 3 apples cost $6, how much do 5 cost? X = (6 x 5) / 3 = $10. When both quantities grow together, the proportion is direct.

Inverse rule of three

Some quantities are inversely proportional: as one rises, the other falls. More workers, less time. Then you keep the same row instead of crossing: X = (A x B) / C. If 4 workers take 6 days, 8 workers take (4 x 6) / 8 = 3 days.

Frequently asked questions

Sources

  • Ratios and proportions (rule of three)

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