Calculators
Square-Root Variation Calculator
Find the constant and a new y value for square-root variation y = k√x from a known pair and a new x value.
For square-root variation, y = k × x^0.5. Enter a known x and y pair and a new x value to find y₂ = k × x₂^0.5. Use positive values from 1e-12 to 1e12. Calculations stay in your browser.
Calculate direct proportionality to a square root.
Square-root variation follows y = k√x, equivalently y = k × x^0.5. Find k = y₁/√x₁, then y₂ = k√x₂. For x₁ = 2 and y₁ = 12, k is approximately 8.48528137424; at x₂ = 4, y₂ is approximately 16.9705627485. Multiplying x by four doubles y; multiplying x by nine triples y. Use this model only when square-root proportionality is established. It does not fit a square-root function with a shift or offset, or infer a model from data. 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 the square root of the x unit. Results use browser floating-point arithmetic rounded to 12 significant digits. 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-root variation?
Divide known y by the square root of known x to find k, then multiply k by the square root of new x. For x = 4 and y = 6, k = 3; at x = 9, y = 9.
What happens when x doubles?
For y = k√x, doubling x multiplies y by √2, approximately 1.4142. Multiplying x by four doubles y.
Can this solve any square-root function?
No. It assumes y = k√x with no horizontal shift or constant offset. A known pair determines k; the calculator does not infer the relationship from data.
Which inputs are supported and are results private?
Enter three positive decimals or scientific notation from 1e-12 to 1e12 inclusive. Zero is excluded because the known x determines k by division. Keep x units consistent. Processing stays in your browser; results display up to 12 significant digits.