Cube Root Calculator

How the Cube Root Calculator Works

The cube root of a number x is the value r that satisfies r × r × r = x. This calculator finds the real cube root of any number — positive, negative, or decimal — tells you whether the input is a perfect cube, and shows the cubing check.

The Formula

∛x = r, where r³ = x

For positive numbers, r is positive; for negative numbers, the real cube root is negative because a negative times a negative times a negative is negative. Numerically, the tool computes r = sign(x) × |x|^(1/3), which works across the full range of inputs.

Worked Example

Find the cube root of 27:

• We look for a number r where r × r × r = 27.
• Testing 3: 3 × 3 × 3 = 27. ✓
• So ∛27 = 3, and because the answer is a whole number, 27 is a perfect cube.

For a non-perfect cube like 50, ∛50 ≈ 3.684, and cubing it back gives roughly 50, confirming the result.

Perfect Cubes to Know

Number	Cube root
1	1
8	2
27	3
64	4
125	5
216	6

Why Cube Roots Matter

Cube roots appear whenever a quantity scales in three dimensions:

• Volume — finding the side length of a cube from its volume.
• Geometry and physics — scaling laws, density, and similar-solid problems.
• Algebra — solving cubic equations and simplifying radical expressions.

Unlike square roots, cube roots accept negative numbers, making them handy across a wider range of problems.