Quick answer
The cube root of x is the number that multiplied by itself three times gives x: ∛x = x^(1/3). ∛27 = 3.
Enter a number. The calculator returns its cube root.
Related tools: Root Calculator: Nth root of a number. Square Root Calculator: Square root with simplified radical form. Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results.
How to use the Cube Root Calculator
- Enter number.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Number | A number | — |
Formula and method
Formula
∛x = x^(1/3)
IEEE-754 double precision; shown to at most 6 decimal places.
Real cube root; negative numbers allowed.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Number = 27.
| Result | Value |
|---|---|
| Cube root | 3 |
Example 2
Inputs: Number = -8.
| Result | Value |
|---|---|
| Cube root | -2 |
Example 3
Inputs: Number = 2.
| Result | Value |
|---|---|
| Cube root | 1.259921 |
The first line is the headline result (cube root). IEEE-754 double precision; shown to at most 6 decimal places.
Negative numbers
Unlike square roots, cube roots of negative numbers are real: ∛(−8) = −2. The cube root of a non-cube such as 10 is irrational, about 2.1544.
Perfect cubes
1, 8, 27, 64, 125, 216, 343, 512, 729 and 1,000 are perfect cubes. Cube roots convert a volume to an edge length: a cube of volume 125 cm³ has sides of 5 cm.
Perfect cubes and volume
∛27 = 3. The first perfect cubes are 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1,000. Most cube roots are irrational: ∛2 ≈ 1.259921.
A cube with volume 64 cm³ has edges of ∛64 = 4 cm. Mathematically, cube roots of negatives are real (∛−8 = −2), unlike square roots.
How the result changes with number
Holding every other input at the first worked example, this table changes only number. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Number | Cube root |
|---|---|
| 13.5 | 2.381102 |
| 27 | 3 |
| 54 | 3.779763 |
| 108 | 4.762203 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number: left empty shows "Enter number." beside that field and no result.
Choosing between the Cube Root Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Root Calculator](/math/root-calculator/) | number and root | 3th root of 27 |
| [Square Root Calculator](/math/square-root-calculator/) | number | √144 |
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Average Calculator](/math/average-calculator/) | numbers | Average (mean) |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Negative numbers have real cube roots
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for number to confirm this.
Frequently asked questions
What is the cube root of 64?
The cube root of 64 is 4, because 4 × 4 × 4 = 64.
How do I estimate ∛50?
Between 3 and 4, about 3.68.
Is a cube root the same as raising to 1/3?
Yes. ∛x and x^(1/3) are the same, so ∛27 = 27^(1/3) = 3.
What is the cube root of 2?
About 1.259921, an irrational number.
How do I find the edge of a cube from its volume?
Take the cube root: a volume of 64 cm³ gives an edge of 4 cm.
What does the Cube Root Calculator calculate?
Cube root of a number. It returns Cube root.
What formula does the Cube Root Calculator use?
∛x = x^(1/3). Real cube root; negative numbers allowed.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Negative numbers have real cube roots.
What is an example of a cube Root result?
With number 27, the cube root is 3.
Related calculators
- Root Calculator — Nth root of a number.
- Square Root Calculator — Square root with simplified radical form.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Average Calculator — Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
- Long Division Calculator — Divide whole numbers to a chosen number of decimal places.
- Reciprocal Calculator — The multiplicative inverse of a number.
- Weighted Average Calculator — Weighted mean of values and weights.
- Least Common Denominator Calculator — Least common denominator of fractions.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.