Cube Root Calculator
Find the cube root of any real number — positive, zero or negative. Unlike the square root, the cube root of a negative number is a real number, so this calculator handles both signs. Choose your precision and see the exact value plus a step-by-step explanation.
Enter a number
Enter a number and press Calculate cube root.
What a cube root is
The cube root of a number n, written ∛n, is the
value that, when cubed (raised to the power 3), equals n:
∛n = x ⟺ x³ = n
For example, ∛27 = 3 because 3³ = 27, and
∛(−8) = −2 because (−2)³ = −8. The cube root of a
negative number is always real, which makes it different from the square root.
Perfect cubes
Numbers such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 and 1331 are perfect cubes — their cube roots are whole numbers. All other real numbers have irrational cube roots.
Key properties
- Sign preservation:
∛(−n) = −∛n. Cube roots preserve the sign of their input, unlike square roots. - Unique value: Every real number has exactly one real cube root (no negative counterpart, unlike square roots).
- Multiplication rule:
∛(a × b) = ∛a × ∛b. - Division rule:
∛(a / b) = ∛a / ∛b(b ≠ 0). - Fractional exponent form:
∛n = n^(1/3).
Common cube roots
| n | ∛n | Type |
|---|---|---|
| 1 | 1 | Perfect cube |
| 8 | 2 | Perfect cube |
| 27 | 3 | Perfect cube |
| 64 | 4 | Perfect cube |
| 125 | 5 | Perfect cube |
| 216 | 6 | Perfect cube |
| 1000 | 10 | Perfect cube |
| −27 | −3 | Negative perfect cube |
| 2 | 1.25992105… | Irrational |
| 10 | 2.15443469… | Irrational |
| 100 | 4.64158883… | Irrational |
| 0.125 | 0.5 | Perfect cube (of 0.5) |
Worked examples
Example 1 — Perfect cube
Calculate ∛125.
5 × 5 × 5 = 125, so ∛125 = 5.
∛125 = 5
Example 2 — Negative cube root
Calculate ∛(−27).
(−3) × (−3) × (−3) = −27, so ∛(−27) = −3.
∛(−27) = −3
Example 3 — Fractional input
Calculate ∛0.008.
0.2 × 0.2 × 0.2 = 0.008, so ∛0.008 = 0.2.
∛0.008 = 0.2
Example 4 — Irrational cube root
Calculate ∛2.
∛2 ≈ 1.2599210498948732… — an irrational number.
∛2 ≈ 1.259921 (rounded to 6 dp)
Common mistakes
-
Confusing cube root with square root.
∛8 = 2(cube root), but√8 ≈ 2.828(square root). Always check which symbol is being used. -
Assuming cube roots of negatives are undefined.
Unlike square roots, cube roots of negative numbers are real:
∛(−8) = −2. -
Writing
∛8 = ±2. The cube root is a single value. Unlike the square root, there is no alternate sign —∛8is unambiguously 2. -
Thinking small numbers have small cube roots.
For values between 0 and 1, the cube root is larger than the
original:
∛0.125 = 0.5.
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Frequently asked questions
The cube root of n is the number whose cube equals n. For example, ∛64 = 4 because 4 × 4 × 4 = 64.
Yes. Unlike the square root, the cube root of a negative number is a real number. ∛(−27) = −3 because (−3)³ = −27.
∛0 = 0, because 0 × 0 × 0 = 0. Zero is the only real number that is its own cube root.
They are inverse operations. Cubing (x³) takes a number and multiplies it by itself three times. Taking the cube root (∛x) finds the number that was cubed to produce the result. For example, 3³ = 27 and ∛27 = 3.
Yes. Every real number has exactly one real cube root. This is different from the square root, where every positive number has two square roots (positive and negative). The cube function is one-to-one on the reals, so its inverse is a single-valued function.