What the rule of three is and when to use it
The rule of three finds a fourth value when you know three others that are in proportion. It's set up as: if A corresponds to B, what does C correspond to? That unknown value is the calculator's X.
Direct proportion
Used when, as one quantity grows, the other grows in the same proportion. Formula: X = B × C ÷ A. Example: if 5 pens cost 20, how much do 8 cost? X = 20 × 8 ÷ 5 = 32.
Inverse proportion
Used when, as one quantity grows, the other shrinks. Formula: X = A × B ÷ C. Example: if 4 workers take 6 days, how long will 8 take? X = 4 × 6 ÷ 8 = 3 days.
How to tell which to use: ask yourself whether “more” of one thing means “more” (direct) or “less” (inverse) of the other. If you're after a percentage, Percentage Calculator solves it in one step.
Frequently Asked Questions
How do I do a simple rule of three?
Cross-multiply and divide: in the direct case, X = B × C ÷ A. Enter A, B and C in the calculator and you get X.
How do I know if it's direct or inverse?
If one quantity grows and the other grows too, it's direct; if the other shrinks, it's inverse.
Is it useful for recipes and prices?
Yes: scaling ingredients for more guests or pricing several units are direct proportion cases.
Can I use decimals?
Yes, with a dot or a comma.