This cube root calculator finds the cube root (∛x) of any number — positive, negative or fractional — and simplifies the radical when the number contains a perfect-cube factor, so ∛54 becomes 3∛2.
What Is a Cube Root?
The cube root of a number is the value that, multiplied by itself three times, gives the number back: ∛27 = 3 because 3 × 3 × 3 = 27. It is the inverse of cubing, and geometrically it recovers the edge length of a cube from its volume — a cube of volume 125 has edges of exactly 5. Unlike square roots, cube roots happily accept negative numbers: ∛(−8) = −2, because (−2)³ = −8. This calculator is part of our Math Calculators collection and the sibling of the Square Root Calculator.
Cube Root Examples (Verified)
- ∛27 = 3 and ∛125 = 5 — perfect cubes.
- ∛100 ≈ 4.642 — between 4³ = 64 and 5³ = 125, closer to 5.
- ∛54 = 3∛2 — 54 = 27 × 2, so the 27 exits as 3.
- ∛(−64) = −4 — negatives work, unlike even roots.
Perfect Cubes Worth Knowing
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| n³ | 1 | 8 | 27 | 64 | 125 | 216 | 343 | 512 | 729 | 1000 |
Recognizing these lets you estimate any cube root instantly: ∛600 sits between 512 and 729, so its root is between 8 and 9 (≈ 8.43).
Cube Roots as Exponents
∛x is x^(1/3) — a fractional exponent, which is how our Exponent Calculator computes it and how all root problems unify: the n-th root of x is x^(1/n). The factoring-out method for simplification also mirrors square roots — just hunt for cube factors (8, 27, 64, 125…) instead of square ones.
Related Tools
- Square Root Calculator
- Exponent Calculator — x^(1/3) and all powers
- Math Calculators — the full collection
Frequently Asked Questions
What is the cube root of 27?
3 — because 3 × 3 × 3 = 27.
Can a cube root be negative?
Yes — uniquely among common roots. A negative number cubed stays negative, so its cube root exists and is negative: ∛(−125) = −5.
How do I simplify a cube root?
Factor out the largest perfect cube: ∛54 = ∛(27 × 2) = 3∛2. This calculator does the factoring automatically for whole numbers.
What is the cube root symbol?
∛ — the radical sign with a small 3 in its notch, indicating the third root.
How do I type a cube root on a calculator?
Use the exponent key: x^(1/3). On this page, just enter the number.
Is this cube root calculator free?
Yes — free, instant, no sign-up.