Inverse Variation in One Step

This inverse variation calculator derives the constant k from one known point (k = x₁y₁) and applies it to a new x to find y₂. The defining property — the product xy stays fixed — is verified in the results for both points.

The Shape of the Curve

Inverse variation plots as a hyperbola: steep near zero and flattening as x grows. Doubling x halves y, tripling x cuts y to a third — the reciprocal scaling that distinguishes inverse from linear or quadratic behavior.

Real-World Applications

Driving time falls as speed rises for a fixed distance, and Boyle's law ties gas pressure inversely to volume. Any physics or economics problem stating "product is constant" is inverse variation in disguise.