Rule of Three Calculator
Solve any proportion: if A corresponds to B, then C corresponds to X. Works with direct proportions (both grow together) and inverse ones (one grows, the other shrinks) — the result appears as you type.
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- Choose the proportion type: direct (more workers, more production) or inverse (more workers, fewer days).
- Fill A and B — the pair you already know.
- Fill C — the new value. X is calculated instantly.
- Direct: X = B × C ÷ A. Inverse: X = A × B ÷ C.
Direct or inverse — how to tell
Ask: when one quantity grows, what happens to the other? If it also grows (more kilos → more money, more hours → more pay), the proportion is direct: X = B × C ÷ A. If it shrinks (more workers → fewer days, more speed → less time), it is inverse: X = A × B ÷ C. Picking the wrong type is the most common mistake — this calculator lets you switch with one click and compare.
Everyday examples
Direct: a recipe for 4 people uses 300 g of rice; for 7 people → 300 × 7 ÷ 4 = 525 g. Direct: a car does 240 km with 20 liters; with 32 liters → 384 km. Inverse: 6 machines finish a job in 10 days; with 8 machines → 6 × 10 ÷ 8 = 7.5 days.
When the rule of three fails
It assumes the relationship is perfectly proportional. Real life sometimes is not: doubling the ingredients of a cake works, but doubling the baking time burns it; ten painters may not paint a wall ten times faster (they get in each other's way). Use the result as a solid estimate and apply common sense to the context.
Frequently asked questions
What is the rule of three formula?
Direct proportion: X = B × C ÷ A. Inverse proportion: X = A × B ÷ C. A and B are the known pair; C is the new value.
How do I know if it is direct or inverse?
If both quantities grow together (more product, more cost), it is direct. If one grows while the other shrinks (more machines, less time), it is inverse.
Can I use decimals?
Yes — all fields accept decimal numbers, and the result keeps the precision.
What about the compound rule of three?
That involves three or more quantities and is solved by chaining simple rules of three. For most everyday problems, the simple rule on this page is enough.