Rule of Three
Direct: A:B :: C:x → x = (B × C) / A · Inverse: x = (A × B) / C
- Fill in three of the four values in the proportion.
- Choose whether the relationship is direct or inverse.
- The missing value is calculated automatically.
In a direct proportion, both quantities grow together. If 3 kilos cost 12, then 5 kilos cost 20 — more kilos, more money.
In an inverse one, a rise on one side means a fall on the other. If 4 people finish a job in 6 hours, 8 people finish in 3 — more people, less time.
Choosing the wrong one is the only way to get a rule of three wrong. Before calculating, ask: if the first value doubles, does the other double or halve?
The rule of three requires genuine proportionality, and not every relationship is proportional.
If 1 painter paints a wall in 4 hours, 100 painters do not finish in 2.4 minutes — they do not all fit on the wall. The inverse relationship holds only within a reasonable range.
Area and volume do not scale linearly either: doubling the side of a square quadruples its area rather than doubling it.
Tiered pricing, progressive taxes and speed under acceleration are other cases where simple proportion breaks down.
Frequently asked questions
Ask what happens if the first value doubles. If the other doubles too, it is direct. If it halves, it is inverse.
You can, treating the total as 100. But the percentage calculator already covers the common cases and is more direct.
Either the relationship is not proportional across the range you used, or the direct/inverse setting is the wrong way round. A hundred painters do not finish a wall a hundred times faster.
Each side of the proportion must keep the same unit. Mixing hours on one side with minutes on the other produces a wrong result with no warning.