Can I take the cube root of a negative number?

Yes. Cube roots are defined for all real numbers. The cube root of −27 is −3 because (−3)³ = −27. This is unlike square roots, which require non-negative inputs for real results.

What is the cube root of 0?

The cube root of 0 is exactly 0, since 0³ = 0.

How is cube root different from square root?

A square root finds y where y² = x and is only real for x ≥ 0. A cube root finds y where y³ = x and is real for any x, including negatives.

How accurate is the result?

Results are computed using JavaScript's native floating-point Math.cbrt() function, which is accurate to about 15 significant digits. The answer is shown rounded to 8 decimal places, and whole-number roots are shown exactly.

What does the radical form show?

The radical form expresses the answer as ∛x, the standard mathematical notation. If the result is a whole number (a perfect cube), the tool highlights that fact.

What are some perfect cubes?

Perfect cubes are numbers whose cube root is a whole integer: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, and so on (1³ through 10³).

Can it simplify a cube root like ∛54?

No. The calculator returns the decimal value (∛54 = 3.77976315) and does not rewrite radicals. To simplify by hand, pull out the largest perfect-cube factor: 54 = 27 × 2, so ∛54 = ∛27 × ∛2 = 3∛2. In the same way, ∛16 = 2∛2 and ∛250 = 5∛2.

How do you find a cube root without a calculator?

Start between two perfect cubes, then refine. ∛100 lies between 4 (4³ = 64) and 5 (5³ = 125), closer to 5, so guess a = 4.6. One Newton step, (2a + x ÷ a²) ÷ 3, gives (9.2 + 100 ÷ 21.16) ÷ 3 = 4.6420, already close to the exact 4.64158883. Repeat the step with the new value for more digits.

Cube Root Calculator

Enter any real number to instantly compute its cube root with full step-by-step working.

The cube root of x is the number y where y × y × y = x, written ∛x or x^(1/3).

Enter a Number

Number (positive, negative, or decimal)

Quick examples

Type a number above to see its cube root.

Step-by-Step Working

Steps will appear here after you enter a number.

Perfect Cubes Reference

∛1 = 1

∛8 = 2

∛27 = 3

∛64 = 4

∛125 = 5

∛216 = 6

∛343 = 7

∛512 = 8

∛729 = 9

∛1000 = 10

Copied to clipboard!

Quick answer

The cube root of x is the number y where y × y × y = x, written ∛x or x^(1/3). Every real number has exactly one real cube root, so negatives work too: ∛−64 = −4. Numbers that are not perfect cubes give decimals, for example ∛2 = 1.25992105 and ∛100 = 4.64158883, rounded to 8 decimal places.

Examples

Number	Cube root	Check
27	3	3³ = 27
−64	−4	(−4)³ = −64
0.125	0.5	0.5³ = 0.125
2	1.25992105	≈ 2
10	2.15443469	≈ 10
100	4.64158883	≈ 100

Type a number or tap one of the quick examples.

Summary

The cube root of a number x is the value y such that y³ = x. Unlike square roots, cube roots exist for all real numbers, including negatives — the cube root of −8 is −2. This tool computes the cube root instantly and walks you through each step of the calculation, from recognizing the sign to verifying the result.

How it works

Enter any real number (positive, negative, or zero) in the input field.
The calculator determines the sign: negative inputs yield a negative cube root.
It computes ∛|x| using the identity ∛x = x^(1/3), then reapplies the sign.
The step-by-step panel shows the full working including the verification check.
Results are shown as a decimal rounded to 8 places and in radical notation, for example ∛(54) = 3.77976315.

Use cases

Find the side length of a cube given its volume.
Solve equations of the form x³ = k in algebra homework.
Verify manual cube root calculations step by step.
Work with negative numbers where square roots are undefined.
Explore cube roots of fractions or decimals.
Check results from scientific calculators.

Frequently Asked Questions

Last updated: 2026-06-04 · Reviewed by Nham Vu