Inverse Variation Calculator

This calculator works out the constant of inverse variation between two quantities and uses it to predict a new value, without you needing to rearrange the formula by hand. Inverse variation describes pairs of numbers that move in opposite directions in a fixed proportion, following the rule y equals k divided by x, so as x doubles, y halves, and their product always equals the same constant k. Everyday examples include speed and travel time over a fixed distance, workers on a job and how long it takes to finish, or pressure and volume of a gas at constant temperature. To use it, enter a known x value and its matching y value, then enter the new x you want to solve for. The calculator multiplies your known pair to find the constant k, shows the relationship as y equals k divided by x, and returns the constant k alongside the predicted y at your new x. It is useful for checking homework, working through science and maths problems, or quickly confirming a proportional relationship without doing the algebra yourself. Keep in mind the calculator assumes a true inverse relationship holds between your two quantities and that you have entered valid, non-zero numbers, since dividing by an x of zero produces an undefined result. The formula, a worked example and the underlying assumptions are set out below.

Known x

Known y

New x

y = 12 / x

Constant k12

Predicted y at new x3

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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