Calculators
Inverse Variation Calculator
Find a new y value and the constant of inverse variation from a known x and y pair and a new x, locally in your browser.
For inverse variation, x × y = k. Enter a known pair and a new x to find y₂ = x₁ × y₁ / x₂. Use positive values from 1e-12 to 1e12. Calculations stay in your browser.
Solve relationships with a constant product.
Inverse variation follows y = k/x, so x₁y₁ = x₂y₂ and y₂ = x₁y₁/x₂. For x₁ = 4 and y₁ = 12, the constant k is 48; when x₂ = 6, y₂ = 8. Doubling x halves y. This model applies only when a constant-product relationship is justified, such as time and speed for a fixed distance. It does not establish a relationship from data or include a nonzero offset. Enter positive values from 1e-12 to 1e12 inclusive; decimals and scientific notation are supported. Zero and negative inputs are excluded. Keep units consistent between the two x values and between the two y values; k has units of x times y. 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 inverse variation?
Find k = x₁ × y₁ from a known pair, then divide k by the new x₂ to get y₂. For (4, 12) and new x = 6, k = 48 and new y = 8.
How is inverse variation different from direct proportion?
Inverse variation keeps the product xy constant: doubling x halves y. Direct proportion keeps y/x constant: doubling x doubles y.
Can I use zero or negative values?
This calculator supports positive values from 1e-12 to 1e12. Zero x makes k/x undefined. Signed inverse-variation 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.