Rule of Three Calculator
Free rule-of-three calculator (cross multiplication) — direct and inverse proportion. Enter three known values, get the fourth. Works in your browser.
Pick direct or inverse proportion, type the three known values, and the calculator returns the missing fourth.
Direct proportion
When two quantities move together — twice as much of A means twice as much of B — the proportion is direct:
A : B :: C : X → X = (B × C) ÷ A
If 2 eggs feed 10 people, 5 eggs feed 25. Both quantities scale by the same factor.
Inverse proportion
When one quantity goes up as the other goes down, the proportion is inverse. What stays constant is the product, not the ratio:
A × B = C × X → X = (A × B) ÷ C
4 workers finish a job in 6 days. 3 workers — less manpower — finish in 8. Total worker-days (4 × 6 = 24) stay the same.
Common mistakes
The single most common error is picking direct when the problem is inverse, or vice versa. Ask: “if I double A, does B double or halve?” That’s the diagnostic.
Worked examples
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Recipe scaling — 2 eggs feed 10, how many people do 5 eggs feed?
If 2 → 10, then 5 → 25.
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Direct: 200 g for 4 servings, what for 7?
If 4 → 200, then 7 → 350.
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Inverse: 4 workers take 6 days; how long for 3?
Inverse: if 4 ↔ 6, then 3 ↔ 8.
Frequently asked questions
What is the rule of three?
A shortcut for solving proportions: when three of the four numbers in a ratio are known, you can compute the fourth. Direct: A is to B as C is to X, with X = (B × C) ÷ A. Inverse: A × B = C × X, with X = (A × B) ÷ C.
When do I use direct vs inverse proportion?
Direct when the two quantities move together — double the recipe, double the flour. Inverse when one goes up as the other goes down — twice as many workers, half the time.
Why does it sometimes give wrong-feeling answers?
Almost always because you mixed up direct and inverse. "More workers, less time" is inverse — adding workers does not multiply the time. Re-check which way the quantities move together.
Does this only work with positive numbers?
Mathematically it works with any numbers, but most real-world proportions are positive. Zeros are rejected (you can't divide by zero); negative inputs give an algebraically-correct but probably-meaningless result.
Where does the rule of three come up in real life?
Recipe scaling, currency / unit conversion sanity checks, fuel and mileage planning, map / scale model ratios, ingredient dilution, dosage, paint coverage, time-and-materials estimates. Anywhere a ratio of two things stays constant or trades off.
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