Free Inverse Variation calculator with clear step-by-step results.
Two quantities vary inversely when their product stays constant: x x y = k. Here the constant is recovered by multiplying the known pair, and the prediction follows from y = k / x. Doubling x therefore halves y, and tripling x cuts y to a third — the exact opposite of direct variation. The curve is a hyperbola that never touches either axis, so both the known and the target x must be non-zero; as x approaches zero, y grows without bound.
Constant product
k = x x y (from the known pair)
Prediction
y_new = k / x_new
In direct variation the ratio y/x is constant, so x and y rise together. In inverse variation the product x times y is constant, so raising x lowers y. Direct variation graphs as a straight line through the origin; inverse variation graphs as a hyperbola.
Multiply x by y for each pair. If every product lands on the same number, the data varies inversely and that number is k. Constant speed over a fixed distance is a classic example: travel time times speed always equals the distance.
y = k / x divides by x, so x = 0 has no defined output. Mathematically the hyperbola has a vertical asymptote there: as x shrinks toward zero, y races off toward infinity.