Calculators
Square Variation Calculator
Find the constant and a new y value for square variation y = kx² from a known pair and a new x value.
For 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 direct proportionality to a square.
Square variation follows y = kx². Find k = y₁/x₁², then y₂ = kx₂², equivalently y₁(x₂/x₁)². For x₁ = 2 and y₁ = 12, k = 3. At x₂ = 4, y₂ = 48. Doubling x multiplies y by four; tripling x multiplies y by nine. Use this model only when square proportionality is established. It does not fit a general quadratic with linear or constant terms. 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 divided by 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 square variation?
Divide known y by known x squared to find k, then multiply k by the new x squared. For x = 2 and y = 12, k = 3; at x = 4, y = 48.
How does this differ from direct or inverse-square variation?
Direct variation y = kx doubles y when x doubles. Square variation y = kx² multiplies y by four. Inverse-square variation y = k/x² divides y by four.
Can this solve any quadratic relationship?
No. This calculator assumes y = kx² with no linear term or constant offset. It uses a known pair rather than fitting a relationship from data.
Which inputs are supported and are results private?
Enter three positive decimals or scientific notation from 1e-12 to 1e12 inclusive. Keep units consistent for x. Calculations stay in your browser and display up to 12 significant digits.