Calculators
Inverse-Cube Variation Calculator
Find the constant and a new y value for inverse-cube variation y = k/x³ from a known pair and a new x value.
For inverse-cube variation, y = k / x³. Enter a known x and y pair and a new x value to find y₂ = k / x₂³. Use positive values from 1e-12 to 1e12. Calculations stay in your browser.
Calculate inverse proportionality to a cube.
Inverse-cube variation follows y = k/x³. Find k = y₁x₁³, then y₂ = k/x₂³. For x₁ = 2 and y₁ = 12, k = 96; at x₂ = 4, y₂ = 1.5. Doubling x divides y by eight; tripling x divides y by 27. Use this model only when inverse-cube proportionality is established. It does not infer a model from data or fit a function with 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 and use consistent y units. The constant has units of y times x cubed. 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 inverse-cube variation?
Multiply known y by known x cubed to find k, then divide k by new x cubed. For x = 2 and y = 12, k = 96; at x = 4, y = 1.5.
What happens when x doubles?
For y = k/x³, doubling x divides y by eight. Tripling x divides y by 27; halving x multiplies y by eight.
Can this determine whether my data follows an inverse-cube model?
No. One known pair determines k only after you assume y = k/x³. This calculator does not fit data or account for offsets.
Which inputs are supported and are results private?
Enter three positive decimals or scientific notation from 1e-12 to 1e12 inclusive. Zero and negative values are excluded. Keep units consistent. Processing stays in your browser; results display up to 12 significant digits.