Start with a known result, then compare the reference and target values for each quantity. Choose whether each quantity changes the result directly or inversely.
Compound Proportion Calculator
Unknown result with several changing quantities
Add between two and five quantities. Compare each one with the result you are trying to find.
| Quantity (optional) | Reference | Target | Relationship |
|---|
How to use the calculator
- Enter the known outcome in Known reference result.
- For each quantity, enter its reference value and the new target value.
- Choose Direct if increasing that quantity increases the result; choose Inverse if it decreases the result.
- Add more quantities if needed, then select Calculate.
What is a compound proportion?
A compound proportion finds an unknown outcome when two or more changing quantities affect it at the same time. Each quantity contributes either a direct ratio (target ÷ reference) or an inverse ratio (reference ÷ target).
X = Y₀ × r₁ × r₂ × … × rn
Test one quantity at a time while holding the others fixed. If increasing it makes the result increase, the relationship is direct. If the result decreases, it is inverse.
Worked example
Four workers, working 6 hours a day, finish a job in 8 days. How many days will 6 workers need if they work 8 hours a day?
| Quantity (optional) | Reference | Target | Relationship |
|---|---|---|---|
| Workers | 4 | 6 | Inverse: More workers means fewer days |
| Hours per day | 6 | 8 | Inverse: More hours per day means fewer days |
Both relationships are inverse: X = 8 × (4 ÷ 6) × (6 ÷ 8) = 4 days.
Frequently asked questions about compound proportions
What is a compound proportion?
It is a calculation used when several quantities influence one unknown result at the same time.
How is it different from a simple proportion?
A simple proportion compares two quantities. A compound proportion combines the effects of two or more changing quantities on the result.
How do I recognize a direct or inverse relationship?
Increase one quantity mentally while keeping everything else fixed. If the result increases, it is direct; if it decreases, it is inverse.
What formula does the calculator use?
It multiplies Y₀ by target/reference for each direct relationship and by reference/target for each inverse relationship.
Can I use decimals?
Yes. Integers and decimals are accepted as long as the units are consistent between reference and target values.
See also…
