Cube Root Calculator

The Cube Root Calculator finds the real cube root of any number — positive, negative, or zero — checks whether it's a perfect cube, shows the two nearest perfect cubes, and simplifies the result to its radical form for whole numbers (like ∛72 = 2∛9).

It's built for students checking homework, teachers preparing examples, and anyone who needs a cube root without reaching for a separate radical-simplification step.

How to use it

1. Enter any number — positive, negative, or zero. Unlike square roots, cube roots of negative numbers are real, so there's no restriction.
2. Read Cube Root for the result.
3. Check Perfect Cube? to see whether the number is a perfect cube, and Simplified Radical Form for the radical written in simplest terms.
4. Nearest Lower/Upper Perfect Cube show the two consecutive perfect cubes your number falls between.

Results update automatically as you type. For example, entering 72 returns a cube root of 4.16017, bounded between 64 (4³) and 125 (5³), with a simplified radical form of 2∛9.

Why can cube roots be negative, unlike square roots?

Every real number has exactly one real cube root, and its sign matches the input's: (-3)³ = -27, so ∛-27 = -3. Square roots don't work this way — squaring always produces a non-negative result, so negative numbers have no real square root. That's why this calculator accepts negative input while the Square Root Calculator doesn't.

What is a perfect cube?

A perfect cube is a number that's the cube of an integer — 1, 8, 27, 64, 125, and so on (or their negatives, like -8 and -27). Its cube root is a whole number with no remaining radical. Any other number has an irrational cube root, which can only be approximated as a decimal or written in simplified radical form.

What does "simplified radical form" mean?

For a whole number that isn't a perfect cube, the cube root can often still be simplified by pulling the largest perfect-cube factor out from under the radical. For example, 72 = 8 × 9, and 8 is a perfect cube, so ∛72 = ∛8 × ∛9 = 2∛9 — a shorter, exact form instead of an infinite decimal. Numbers with no perfect-cube factor greater than 1 (like 9 or 10) are already in simplest form.

Need a root of a different degree — square, fourth, fifth, or beyond? Use the Nth Root Calculator, which handles any degree from 1 to 100 with adjustable precision.

To see the prime factors this calculator's simplification step is built on, try the Prime Factorization Calculator.

Privacy

This calculator runs entirely in your browser. Your number is never uploaded, logged, or stored — the computation happens locally on your device.