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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y = 3 x
Constant k3
Predicted y at new x15

The formula

Direct variation has the form y = k x, where k is the constant of variation. Find k from a known pair as k = y / x, then predict any y from y = k x. The graph is a straight line through the origin.

Worked example

If y = 6 when x = 2, then k = 6 / 2 = 3, so y = 3x. At x = 5, y = 3 times 5 = 15. Enter 2, 6 and 5 to confirm.

Frequently asked questions

What is direct variation?

A relationship where y = kx, so y is a constant multiple of x and the two are proportional.

How do I find the constant k?

Divide a known y by its matching x. That ratio is the same for every pair in a direct variation.

What does the graph look like?

A straight line through the origin with slope k.

Who this calculator is for

This calculator is for students and anyone needing a quick, reliable result.

What this calculator assumes

  • You enter valid numbers.
  • The standard formula is applied.
  • Results are rounded for display.

Formula and sources

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