Direct Variation Calculator

Solve direct variation problems with y = kx and find the predicted y value for a new x.

Last updated: June 2026 | By Patchworkr Team

Variation Solver

Known y

Known x

New x

Results

y = kx

k = 5

y = 25

Using x = 5, the predicted y is shown above.

k = y / x = 10 / 2 = 5; y = kx = 5 × 5 = 25

What is Direct Variation?

In direct variation, one variable is always a constant multiple of the other. The equation is y = kx.

If y = 12 when x = 3, then k = 4 and y = 40 when x = 10.

What if x is zero?

If x is zero and y is not zero, direct variation does not work. If both are zero, k is not determined.

Can k be negative?

Yes. A negative k still gives a direct variation because y stays proportional to x.

Do decimals work?

Yes. The calculator accepts decimals and scientific notation as long as the values are finite.

Is the new y value exact?

Yes, it is the value produced by y = kx using the inputs you provided.

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