Direct Variation Calculator

This direct variation calculator helps you work with two quantities that rise and fall together in a fixed ratio, following the rule y equals k times x, where k is the constant of variation. Direct variation shows up whenever doubling one amount doubles the other, such as the cost of items at a fixed unit price, the distance covered at a steady speed, or ingredients scaled up in a recipe. You enter a known pair of values, a known x and its matching known y, and a new x you want to predict the y for. From that pair the calculator divides y by x to find the constant k, then multiplies k by your new x to predict the matching y. The results show the full relationship as y equals k times your new x, the constant k on its own, and the predicted y at the new x you entered. This makes it quick to check homework, extend a pattern, or scale a real-world rate without doing the division and multiplication by hand. Because k is found by dividing y by x, the known x you enter cannot be zero, and results update instantly as you change any of the three figures. The formula, a worked example and answers to common questions on direct variation and proportional relationships follow below.

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