Calculators

Cube-Root Variation Calculator

Find the constant and a new y value for cube-root variation y = k∛x from a known pair and a new x value.

For cube-root variation, y = k × x^(1/3). Enter a known x and y pair and a new x value to find y₂ = k × x₂^(1/3). Use positive values from 1e-12 to 1e12. Calculations stay in your browser.

Enter known x and y values and a new x value, then calculate.

Calculate direct proportionality to a cube root.

Cube-root variation follows y = k∛x, equivalently y = k × x^(1/3). Find k = y₁/∛x₁, then y₂ = k∛x₂. For x₁ = 8 and y₁ = 6, k = 3; at x₂ = 27, y₂ = 9. Multiplying x by eight doubles y; multiplying x by 27 triples y. Use this model only when cube-root proportionality is established. It does not fit a shifted cube-root function or infer a model from data. This calculator accepts three positive values from 1e-12 to 1e12 inclusive, including decimals and scientific notation; zero and negative inputs are excluded even though cube roots of negative numbers exist. Keep old and new x in the same units. The constant has units of y divided by the cube root of the x unit. Browser floating-point results are 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 cube-root variation?

Divide known y by the cube root of known x to find k, then multiply k by the cube root of new x. For x = 8 and y = 6, k = 3; at x = 27, y = 9.

What happens when x doubles?

For y = k∛x, doubling x multiplies y by the cube root of two, approximately 1.2599. Multiplying x by eight doubles y.

Can this solve any cube-root function?

No. It assumes y = k∛x without shifts or offsets. One known pair determines k but does not establish the model from data.

Are negative values supported and are results private?

This calculator accepts only positive values from 1e-12 to 1e12 inclusive, although negative numbers have real cube roots. Decimals and scientific notation are supported. Keep x units consistent. Processing stays in your browser and results display up to 12 significant digits.