Calculators

Direct Variation Calculator

Find a new y value and the constant of proportionality from a known direct variation pair and a new x, locally in your browser.

For direct variation, y ÷ x = k. Enter a known pair and a new x to find y₂ = k × x₂. Use positive values from 1e-12 to 1e12. Calculations stay in your browser.

Enter a known pair and a new x value, then calculate.

Solve relationships with a constant ratio.

Direct variation follows y = kx, so y/x is constant: y₁/x₁ = y₂/x₂ and y₂ = (y₁/x₁) × x₂. For x₁ = 4 and y₁ = 12, the constant of proportionality k is 3; when x₂ = 6, y₂ = 18. Doubling x doubles y, and negative k would make y decrease as x increases. The graph is a straight line through the origin, with no y-intercept. This calculator finds k and a new y from a known pair; it does not fit a line from data or prove that two quantities vary directly. Enter positive values from 1e-12 to 1e12 inclusive; decimals and scientific notation are supported. Zero and negative inputs are excluded so k stays defined and positive. Keep units consistent between the two x values and between the two y values; k has units of y per x. Results use browser floating-point arithmetic rounded to 12 significant digits. Inputs stay in your browser.

Frequently Asked Questions

Everything you need to know about this tool, how it works, and privacy.

How do I calculate direct variation?

Find k = y₁ / x₁ from a known pair, then multiply k by the new x₂ to get y₂. For (x₁ = 4, y₁ = 12) and new x₂ = 6, k = 3 and new y₂ = 18.

How is direct variation different from inverse variation?

Direct variation keeps y/x constant, so doubling x doubles y. Inverse variation keeps xy constant, so doubling x halves y.

Can I use zero or negative values?

This calculator supports positive values from 1e-12 to 1e12. Zero x makes the constant y/x undefined, and signed proportional relationships are outside this tool’s input scope.

Are the results exact and private?

Results use floating-point arithmetic rounded to 12 significant digits. Calculations and copying run in your browser without uploading or storing inputs.