Direct Variation Calculator

This direct variation calculator works with quantities that are directly proportional, where y equals a constant times x. Enter a known x and y pair and the calculator finds the constant of variation k, then uses it to predict y for any new x you enter. Direct variation describes situations where doubling one quantity doubles the other, such as cost and quantity at a fixed price, or distance and time at a steady speed. The constant k is the rate that links them. The formula, a worked example and the assumptions are set out below.

Known x

Known y

New x

Constant k

Predicted y at new x

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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Scientific Calculator: general scientific maths.
Percentage Calculator: percentages and changes.
Ratio Calculator: simplify and scale ratios.

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