Inverse Proportion Calculator

When the product stays constant instead of the ratio.

When the product stays constant instead of the ratio. In inverse proportion the product stays constant: x × y = k throughout.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

First quantity

First result

Second quantity

Second result

Constant product k = 24

Constant of proportionality (k)24

Second result3

Ratio of quantities2 ×

Ratio of results0.5 ×

Direct proportion would give12

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

Where to go next

The Inverse Proportion question rarely arrives on its own. These are the ones that usually come with it:

Proportion Calculator — Solve a : b = c : d for whichever term is missing.
Ratio Calculator — Simplify a ratio, and see it as shares of the whole.
Harmonic Mean Calculator — The right average for speeds and rates.
Percentage Calculator — Every common percentage question in one place.

Sources

NIST Digital Library of Mathematical Functions

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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