Math
Cube Root Calculator
Enter any number to get its cube root.
Perfect cubes return exact whole or decimal answers, other integers are simplified into radical form (∛54 = 3∛2) alongside the decimal, and negative inputs work because odd roots of negatives are real. The steps show the prime factorization, the perfect-cube factor pulled out, and a check by cubing the answer.
Any real number up to 1 trillion in size. Negatives and decimals are allowed.
Try an example
Result
Cube root
—
- Decimal value
- —
- Simplified radical
- —
- Perfect cube?
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- Nearest perfect cubes
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Study path
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What the cube root calculator solves
Enter any number to get its cube root. Perfect cubes return exact whole or decimal answers, other integers are simplified into A root expression written with the √ symbol, such as a square root. form (∛54 = 3∛2) alongside the decimal, and negative inputs work because odd roots of negatives are real. The steps show the A whole number above 1 whose only factors are 1 and itself. factorization, the perfect-cube factor pulled out, and a check by cubing the answer.
Formula
How to use it
- Enter the number (positive, negative, whole, or decimal).
- Read the cube root: an exact integer or decimal for perfect cubes, or simplified radical form plus a decimal otherwise.
- Use the nearest perfect cubes to estimate the answer by hand, and the check line to confirm it.
How to read the answer
The cube root of x is the number that multiplies by itself three times to give x. If the input is a perfect cube the answer is exact; otherwise the simplified radical is the The answer kept as a fraction or radical instead of a rounded decimal. and the decimal is a rounded approximation. Because (-2)³ = -8, negative inputs have real negative cube roots, unlike square roots.
Common mistakes and edge cases
- Treating ∛-27 as undefined. Odd roots of negatives are real: ∛-27 = -3.
- Pulling out pairs instead of triples: ∛16 = 2∛2 because only one group of three 2s exists in 2⁴.
- Confusing ∛x with x/3 or with √x.
- Reading the decimal as exact: ∛2 ≈ 1.259921 never terminates or repeats.
- Forgetting that ∛(a × b) = ∛a × ∛b holds but ∛(a + b) ≠ ∛a + ∛b.
Worked examples
∛54
54 = 2 × 3³, so ∛54 = 3∛2 ≈ 3.7798.
Cube root
3∛2 ≈ 3.779763
Perfect cube ∛729
9³ = 729.
Cube root
9
Negative ∛-64
(-4)³ = -64.
Cube root
-4
Decimal perfect cube ∛0.008
0.2³ = 0.008.
Cube root
0.2
Zero
∛0 = 0.
Cube root
0
Non-cube decimal
∛2.5 ≈ 1.3572.
Cube root
1.357209
Frequently asked questions
What is the cube root of 54?+
∛54 = 3∛2 ≈ 3.7798. Since 54 = 27 × 2 and 27 = 3³, one 3 comes out of the radical and 2 stays inside.
Can a cube root be negative?+
Yes. A negative number cubed stays negative, so ∛-8 = -2 and ∛-64 = -4. This is different from square roots, which have no real value for negatives.
How do I know if a number is a perfect cube?+
Factor it into primes; every prime must appear a multiple of three times. 216 = 2³ × 3³ is a perfect cube (6³), while 54 = 2 × 3³ is not.
How do you find a cube root by hand?+
Find the nearest perfect cubes: 3³ = 27 and 4³ = 64 bracket 54, so ∛54 is between 3 and 4 and closer to 4. Refine with a guess-and-check or Newton's method: y ← (2y + x/y²)/3.
What is the cube root of a decimal like 0.008?+
Write it as 8/1000. Both are perfect cubes, so ∛0.008 = 2/10 = 0.2.
Is the cube root the same as raising to the 1/3 power?+
Yes for real numbers: ∛x = x^(1/3). The calculator shows this rational-exponent form next to the radical form.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026