Inverse Proportion Calculator
When the product stays constant instead of the ratio.
Work out Inverse Proportion. When the product stays constant instead of the ratio. Shows the working, not just the answer.
Second result
3
Constant product k = 24
In inverse proportion the product stays constant: x × y = 24 throughout. Multiplying the quantity by 2 therefore divides the result by the same factor. The last row shows what direct proportion would have given — 12 — which is the answer people reach for by habit and the reason twice the workers rarely means twice the time.
How the Inverse Proportion Calculator works
In inverse proportion the product stays constant: x × y = k throughout. Multiplying the quantity by three therefore divides the result by three. The page also shows what direct proportion would have given, since that is the answer people reach for by habit.
Also known as: inversely proportional calculator · inverse variation calculator · indirect proportion calculator · inverse proportion formula
Frequently asked questions
What is inverse proportion?
A relationship where one quantity rises as the other falls, keeping their product fixed. Four workers taking 6 hours means eight workers take 3.
How do I solve an inverse proportion?
Multiply the first pair to get the constant, then divide it by the new quantity. 4 × 6 = 24, and 24 ÷ 8 = 3.
What is the constant of proportionality?
The fixed product, k. It carries the meaning of the problem — in a work problem it is the total labour required regardless of how many people share it.
Does twice the workers always halve the time?
Only in the idealised model. Real work has coordination costs and tasks that cannot be split, which is why this arithmetic is a starting point rather than a promise.
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<iframe src="https://www.thecalclibrary.com/embed/inverse-proportion-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Inverse Proportion Calculator"></iframe>The only condition is that the credit line stays visible. It sits inside the frame, so you do not have to do anything to keep it.