∛ Cube Root Calculator
Cube Root Calculator
Use the calculator above to find the cube root of any real number (positive, negative, or decimal). See below the step-by-step method using Newton's iteration, plus a table of common perfect cubes.
Formula
The cube root of a number a is the value x such that:
x3 = a ⇔ ∛a = x
Every real number has exactly one real cube root. Unlike the square root, the cube root is defined for negative inputs: ∛(−a) = −∛a.
How to Calculate Cube Roots
For perfect cubes (8, 27, 64, 125, …) the cube root is an integer — just recall the cube of small integers.
For other numbers, use Newton's Method:
- Start with a rough estimate (e.g. x0 = a / 3).
- Apply xn+1 = (2xn + a/xn2) / 3.
- Repeat 3–4 times — the value converges fast (each step roughly doubles the digits of precision).
Common Cube Roots
Perfect Cube Roots Table
Common perfect cubes from 1 to 1000. For the full table 1–100, see our cube root chart 1 to 1000.
| n | ∛n |
|---|---|
| 1 | 1 |
| 8 | 2 |
| 27 | 3 |
| 64 | 4 |
| 125 | 5 |
| 216 | 6 |
| 343 | 7 |
| 512 | 8 |
| 729 | 9 |
| 1000 | 10 |
Popular Cube Root Calculations
Top cube root calculations based on search data:
Related Calculators
- Simplify Cube Root — radical form (e.g. ∛24 = 2∛3)
- Cube (n3) Calculator — the inverse operation
- Is N a Perfect Cube? — check any integer (incl. negatives)
- Square Root Calculator — decimal square root