Cube Root Calculator
The cube root of any number — the value that multiplied by itself three times gives what you entered.
The cube root of x, written ∛x, is the number that cubed gives x.
How the cube root calculator works
The cube root of x, written ∛x, is the number that cubed gives x. Unlike square roots, cube roots work for negative numbers too: ∛−8 is −2, because −2 × −2 × −2 = −8. Cube roots turn a volume back into a side length, which is why they appear whenever you scale something in three dimensions.
Formula: ⁿ√x = x^(1/n)
Worked examples
| Inputs | Root | Note |
|---|---|---|
| ∛27 | 3 | 3 — a perfect cube |
| ∛1000 | 10 | 10 |
| ∛2 | 1.2599210499 | 1.2599 — the classic doubling-the-cube problem |
FAQFrequently asked questions
What is a cube root?
The number that multiplied by itself three times gives yours: ∛125 = 5.
Can a cube root be negative?
Yes — ∛−27 is −3. Unlike square roots, negatives are fine because an odd power keeps the sign.
Which numbers are perfect cubes?
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
How do I find a side length from a volume?
Take the cube root: a cube holding 1,000 cm³ has 10 cm sides.
Why does doubling a box need more than double the side?
Because volume grows with the cube. To double it you multiply the side by ∛2, about 1.26.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.