Inverse Variation Calculator

This inverse variation calculator works with quantities that are inversely proportional, where y equals a constant divided by x. Enter a known x and y pair and the calculator finds the constant k, then predicts y for any new x. In inverse variation, as one quantity goes up the other comes down in proportion, so their product stays fixed. Familiar examples include speed and travel time over a set distance, or the number of workers and the time a job takes. The formula, a worked example and the assumptions are set out below.

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Known x

Known y

New x

Constant k

Predicted y at new x

The formula

Inverse variation has the form y = k / x, equivalently x times y = k. Find k from a known pair as k = x times y, then predict any y from y = k / x. The graph is a hyperbola.

Worked example

If y = 6 when x = 2, then k = 2 times 6 = 12, so y = 12 / x. At x = 4, y = 12 / 4 = 3. Enter 2, 6 and 4 to confirm.

Frequently asked questions

What is inverse variation?

A relationship where y = k / x, so the product of x and y is the constant k.

How do I find k?

Multiply a known x by its matching y. That product is the same for every pair.

What is an everyday example?

Speed and time for a fixed distance: go twice as fast and the trip takes half as long.

Who this calculator is for

This calculator is for students and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid numbers.
The standard formula is applied.
Results are rounded for display.

Formula and sources

Related calculators

Scientific Calculator: general scientific maths.
Percentage Calculator: percentages and changes.
Ratio Calculator: simplify and scale ratios.

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