About the Cube Root Calculator
What is the Cube Root Calculator?
The cube root of x, written ∛x, is the number that multiplied by itself three times gives x: ∛343 = 7 because 7 × 7 × 7 = 343. Unlike square roots, cube roots of negative numbers are real: ∛−27 = −3.
Cube roots appear when working backwards from a volume — the side of a cube holding 1,000 litres (1 m³) is ∛1 = 1 m — and in scaling problems, where doubling every length multiplies the volume by 8.
How to use the Cube Root Calculator
- Number (can be negative) — any real number — positive, negative or decimal. (sample: 343)
- Press Find Cube Root (results also refresh as you type). The result card shows the Cube Root, along with Perfect cube? and Check: root³.
Formula used
∛x = x^(1/3)
- x = the number whose cube root you want
For negative x the calculator uses ∛x = −∛|x|. Answers within rounding error of a whole number are reported exactly, so ∛343 shows 7 rather than 6.99999999.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Number (can be negative) | 343 |
| Result | Value |
|---|---|
| Cube Root | 7 |
| Perfect cube? | Yes |
| Check: root³ | 343 |
Tips for using the Cube Root Calculator
- Perfect cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000.
- ∛(a × b) = ∛a × ∛b, which helps simplify: ∛54 = ∛27 × ∛2 = 3∛2.
- Volume scales with the cube of length, so the cube root of a volume ratio gives the length ratio.