Perfect Cube Calculator — Check & Find Cube Roots
Enter any integer to find out if it is a perfect cube, what its cube root is, and which perfect cubes surround it.
Perfect cube — the cube root is an exact integer
- 1
Cube root ∛|n|
∛27 = 3 - 2
Round to nearest integer k
3 - 3
Verify k³ = |n|
3 × 3 × 3 = 27Equals n → perfect cube - 4
Cube root ∛n
3
How does this calculator work?
n is a perfect cube when its cube root ∛n is an exact integer k (so k³ = n). Enter n and the calculator checks this, shows k if it exists, or identifies the adjacent perfect cubes k³ and (k+1)³ when n is not a perfect cube. Negatives are supported because (−k)³ = −k³.
Formula
How this is calculated
A perfect cube is an integer that can be expressed as k³ for some integer k. The first few are 0, 1, 8, 27, 64, 125, … and negative perfect cubes are −1, −8, −27, … because (−k)³ = −k³.
The calculator computes the real cube root of |n| and checks whether rounding it to the nearest integer gives an exact cube. Integer arithmetic is used for the final check — roundedK³ === |n| — so floating-point rounding in the cube-root computation does not cause false results for reasonable input sizes.
If n is not a perfect cube, the calculator identifies the two perfect cubes it falls between by taking the floor of ∛|n|. The cube root displayed for non-perfect-cubes is the true real-valued ∛n, which is irrational for most inputs. There is no upper size limit, though very large integers may lose precision because JavaScript numbers are IEEE 754 doubles with about 15–16 significant decimal digits.
Frequently asked questions
0, 1, 8, 27, 64, 125, 216, 343, 512, 729. They are 0³ through 9³. The negatives −1, −8, −27 … are also perfect cubes.
Not necessarily. A number that is both a perfect square and a perfect cube must be a perfect sixth power (e.g. 64 = 2⁶). The sequences overlap but are mostly distinct.
Yes. Because (−k)³ = −k³ for any positive integer k, all negative perfect cubes exist: −1, −8, −27, −64, … The calculator handles negative inputs correctly.
Also known as
TG we-Calculate Editorial Team. (2026). Perfect Cube Calculator — Check & Find Cube Roots [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/perfect-cube-calculator
TG we-Calculate Editorial Team. "Perfect Cube Calculator — Check & Find Cube Roots." TG we-Calculate. 2026. https://we-calculate.com/calculator/perfect-cube-calculator.
TG we-Calculate Editorial Team, "Perfect Cube Calculator — Check & Find Cube Roots," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/perfect-cube-calculator
@misc{wecalculate_perfect_cube_calculator, title = {Perfect Cube Calculator — Check & Find Cube Roots}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/perfect-cube-calculator}}, year = {2026}, note = {TG we-Calculate} }
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