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Calculator Answers

Cube Root Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A cube root calculator computes the value that, when multiplied by itself twice (cubed), yields the original number. Unlike square roots, real cube roots are defined for all real numbers, including negative values. The calculator rounds decimal results to your preferred precision and checks whether the input is a perfect cube.

Find the cube root ∛x of any positive or negative real number. Includes decimal precision controls and perfect cube validations.

Quick Answer

Calculate the cube root ∛x of any real number. Enter a positive, negative, or decimal value to find the number that, cubed, equals your input.

The number to find the cube root of. Works for positive and negative numbers. · e.g. 27

Decimal places
Cube Root

Cube Root ∛x

3

27 is a perfect cube

Input x27
Cube root3
Rounded (6 dp)3
Perfect cubeYes

27 is a perfect cube. ∛27 = 3 because 3 × 3 × 3 = 27.

Step-by-step solution

Step 1:∛x = y where y³ = x
Step 2:∛(27) = y where y³ = 27
Step 3:y = 3 since 3³ = 27
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Examples

∛27

= 3

∛-8

= -2

∛64

= 4

∛125

= 5

How it works

The Cube Root Operation

The cube root of a number x is written as ∛x or x1/3. It satisfies:

∛x = y where y³ = x

Because any real number has exactly one real cube root, the function is defined across all positive, negative, and zero real inputs.

To compute second-order roots, check our standard square root calculator or use our absolute value calculator for general numerical magnitude checks.

Table of perfect cubes (1 to 10)

Number (y)Cube (y³)Cube Root (∛x)
11∛1 = 1
28∛8 = 2
327∛27 = 3
464∛64 = 4
5125∛125 = 5
6216∛216 = 6
7343∛343 = 7
8512∛512 = 8
9729∛729 = 9
101000∛1000 = 10

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More tools from Education

Square Root CalculatorCalculate the square root of any number with step by step work. Find the decimal value, simplified radical form, and perfect square check. Works as a square root calculator, sqrt calculator, radical calculator, perfect square calculator, simplify square root tool, and reference for the square root formula. Useful for calculate square root problems and square root examples in algebra and geometry.

Frequently asked questions

The cube root of a number x is a number y such that y cubed (y × y × y) equals x. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27.

Yes. Unlike square roots, cube roots are defined for negative numbers in the real number system. This is because multiplying three negative numbers yields a negative result. For example, ∛−8 is −2 because (−2) × (−2) × (−2) = −8.

A square root asks what number multiplied by *itself* once equals the value: √9 = 3 (since 3 × 3 = 9). A cube root asks what number multiplied by itself *twice* equals the value: ∛27 = 3 (since 3 × 3 × 3 = 27). Additionally, square roots of negative numbers require imaginary numbers, while negative cube roots are real numbers.

A perfect cube is an integer whose cube root is also an integer. Examples include 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.