RootLab

Cube Root Calculator

∛n and n³ together.

Number

Cube root

∛n

Cubed: 19,683

What you entered

Number: 27

1
Take the cube root
∛27= 3
2
Check: cube it back
3³= 27

Result

Cube root: 3

The cube root of 27 is 3.

Cube roots of common numbers

The cube root is the value that multiplied by itself three times gives the original number.

Number	Cube root	Number cubed
8	2.000000	512
10	2.154435	1000
27	3.000000	19683
64	4.000000	262144
100	4.641589	1000000
125	5.000000	1953125
216	6.000000	10077696
1000	10.000000	1000000000

Perfect cubes - 8, 27, 64, 125, 216 and 1000 - give whole-number roots, and they thin out much faster than perfect squares because they grow with the cube. Unlike square roots, cube roots of negative numbers are perfectly well defined: the cube root of -8 is -2, since -2 cubed is -8. Cube roots matter whenever you scale a volume back to a length - working out the side of a cubic tank from its capacity, or the radius of a sphere from how much it holds.

How to calculate cube roots

The cube root of a number n is the value x such that x³ = n. For perfect cubes it's a whole number: ∛27 = 3, ∛64 = 4, ∛125 = 5. For non-perfect cubes like ∛50 ≈ 3.684, you need a calculator or the estimation method of narrowing between known cubes.

Cube roots of negative numbers

Unlike square roots, every real number has exactly one real cube root — including negatives. Since (−2)³ = −8, it follows that ∛(−8) = −2. This is because a negative times a negative times a negative is negative.

Common perfect cubes to memorize

The first 10 perfect cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000. Knowing these lets you estimate any cube root by finding which two perfect cubes your number falls between — for example, ∛100 is between ∛64 = 4 and ∛125 = 5, closer to 5.

Cube roots in real-world problems

Cube roots appear whenever you reverse a volume calculation: given a box's volume, find its side length. They're also used in physics (relating energy to force), engineering (flow rates through pipes), and statistics (geometric means of three values).

Frequently asked questions

What is the cube root of a number?

The cube root of n (written ∛n) is the number that, when multiplied by itself three times, equals n. For example, ∛27 = 3 because 3 × 3 × 3 = 27. Every real number, including negatives, has exactly one real cube root.

How do you estimate a cube root without a calculator?

Find the two perfect cubes your number falls between. For ∛200: since 5³ = 125 and 6³ = 216, the answer is between 5 and 6, close to 6. Then refine: 5.8³ = 195.1, 5.85³ = 200.0 — so ∛200 ≈ 5.85.

Can you take the cube root of a negative number?

Yes. Unlike square roots, cube roots of negative numbers are real. ∛(−8) = −2 because (−2) × (−2) × (−2) = −8. The cube root function works for all real numbers.

What is the difference between cube root and square root?

A square root undoes squaring (x²), while a cube root undoes cubing (x³). Square roots of negative numbers are not real, but cube roots of negatives are. Every real number has one real cube root but may have zero or two real square roots.