Inverse Variation Calculator

About this calculator

Two quantities are in inverse variation when their relationship follows y = k / x, meaning their product stays constant at k, so as x increases y decreases proportionally, and doubling x always halves y. Given one known pair of x and y values, the constant is found by rearranging to k = x × y, and once k is known it predicts y for any new value of x.

This pattern shows up whenever two factors trade off to keep a total fixed: at a constant temperature, gas pressure and volume trade off according to Boyle’s Law (P × V = constant); the time to complete a fixed amount of work decreases as the number of workers increases; and travel time decreases as speed increases for a fixed distance.

Enter a known x and y pair to find the constant k, then enter a new x value and this calculator predicts the corresponding y using the same inverse relationship.