Compound rule of three calculator
Solve problems where two quantities vary at once (machines, days, output...), directly or inversely.
Direct: more machines → more parts. Inverse: more machines → fewer days. Each quantity's fraction goes upright when direct and flipped when inverse.
How the calculation works
In the compound rule of three, the known value is multiplied by a fraction for each quantity that changed: x = base × (new/old) when the relation is direct, and × (old/new) when inverse.
Classic example: 6 machines in 10 days make 1,000 parts. How many parts do 8 machines make in 15 days? Both direct: x = 1000 × (8/6) × (15/10) = 2,000 parts.
Examples
- 6 machines in 10 days → 1,000 parts. With 8 machines in 15 days (both direct): 1000 × 8/6 × 15/10 = 2,000 parts.
- 4 workers take 12 days. With 6 workers (inverse): 12 × 4/6 = 8 days.
Frequently asked questions
How do I know if it's direct or inverse?
Ask: if this quantity grows, does the result grow or shrink? Grows → direct. Shrinks → inverse (e.g., more workers → fewer days).
What about three varying quantities?
Same method: one fraction per quantity. Run it twice: use this result as the base and add the third quantity.
How does it differ from the simple rule of three?
The simple one has only two quantities (one proportion). The compound one involves three or more, each with its own direct or inverse relation to the result.
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Updated on July 5, 2026 · by Rafael Rossi · Methodology & sources