Calculators
Inverse-Square Variation Calculator
Find the constant and a new y value for inverse-square variation y = k/x² from a known pair and a new x value.
For inverse-square variation, y = k / x². Enter a known x and y pair and a new x value to find y₂ = k / x₂². Use positive values from 1e-12 to 1e12. Calculations stay in your browser.
Calculate how a quantity changes with the inverse square.
Inverse-square variation follows y = k/x². Find k = y₁x₁², then y₂ = k/x₂², equivalently y₁(x₁/x₂)². For x₁ = 2 and y₁ = 12, k = 48. At x₂ = 4, y₂ = 3. Doubling x divides y by four; tripling x divides y by nine. Use this model only when inverse-square proportionality is established; this calculator does not infer a relationship from data or include an offset. Enter three positive values from 1e-12 to 1e12 inclusive. Decimals and scientific notation are supported; zero and negative inputs are excluded. Keep old and new x in the same units. The constant has units of y times x squared. Results use browser floating-point arithmetic rounded to 12 significant digits. All calculations 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-square variation?
Multiply known y by known x squared to find k, then divide k by the new x squared. For x = 2 and y = 12, k = 48; at x = 4, y = 3.
How is this different from inverse variation?
Inverse variation uses y = k/x, so doubling x halves y. Inverse-square variation uses y = k/x², so doubling x divides y by four.
Which inputs are supported?
Enter three positive decimal numbers or scientific notation from 1e-12 to 1e12 inclusive. Use the same units for old and new x. Zero and negative inputs are excluded.
Are the results private and exact?
Calculations stay in your browser. Results use floating-point arithmetic displayed to 12 significant digits.