Direct Variation Calculator

About this calculator

Two quantities are in direct variation when their relationship can be written as y = kx, meaning y grows in exact proportion to x through a fixed constant k, so doubling x always doubles y. Given one known pair of x and y values, the constant of variation is found by isolating k = y / x, and once k is known it predicts y for any new value of x, or x for any new value of y.

This is one of the first proportional-relationship models taught in algebra, and it describes many real-world quantities: distance traveled at constant speed equals speed times time, the cost of buying items at a fixed unit price equals price times quantity, and currency conversion at a fixed exchange rate all follow the same y = kx pattern.

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 that same proportional relationship.