Cube Root Calculator — ∛x Instantly
Enter any real number — positive, negative or zero — to get its cube root, a verification check, step-by-step working and a y = ∛x curve with the result highlighted.
∛27 = 3
Input
Formula
Result
Verification
- 1
Take the cube root
∛27 = ∛27 = 3 - 2
Verify: cube the result
(3)³ = 27Should equal the original input; tiny floating-point rounding is normal.
How does this calculator work?
The cube root of x equals x raised to the power 1/3. It is defined for all real numbers (including negatives), unlike the square root. Enter x to get ∛x instantly — the calculator also shows verification (∛x)³, step-by-step working, and the y = ∛x curve with your result highlighted.
Formula
How this is calculated
The cube root of a number x is the value y such that y³ = x. Equivalently, ∛x = x^(1/3). Because raising any real number to the power 1/3 is defined for all real inputs — including negatives — the cube root exists for every real number, unlike the square root. For negative inputs this calculator applies the real-valued convention ∛(−x) = −∛x rather than returning a complex result (e.g., ∛(−27) = −3).
Computation uses JavaScript's built-in Math.cbrt function, which computes the correctly-rounded IEEE 754 double-precision cube root. For verification, the result is cubed and displayed; minor floating-point rounding (e.g., 26.999999… instead of 27) is normal and not an error.
The graph plots y = ∛x over a range centred on your input so you can see the shape of the function — it is strictly increasing, passes through the origin, and is symmetric under a 180° rotation about the origin (an odd function). The highlighted dot marks your specific input/output pair.
Frequently asked questions
The real cube root of a negative number is negative: ∛(−8) = −2, because (−2)³ = −8. This is different from square roots, which have no real solution for negative inputs. Complex cube roots also exist but are not shown here.
Yes, for real numbers. ∛x = x^(1/3). In programming and spreadsheets you can write =x^(1/3) or POWER(x, 1/3), though for negative x some implementations return an error rather than the real cube root — use ABS(x)^(1/3) with a sign correction in those cases.
A perfect cube is an integer whose cube root is also an integer: 1 (∛1=1), 8 (∛8=2), 27 (∛27=3), 64 (∛64=4), 125 (∛125=5), 216, 343, 512, 729, 1000, and so on. Non-perfect cubes like 2, 3, 5 have irrational cube roots.
TG we-Calculate Editorial Team. (2026). Cube Root Calculator — ∛x Instantly [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cube-root-calculator
TG we-Calculate Editorial Team. "Cube Root Calculator — ∛x Instantly." TG we-Calculate. 2026. https://we-calculate.com/calculator/cube-root-calculator.
TG we-Calculate Editorial Team, "Cube Root Calculator — ∛x Instantly," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cube-root-calculator
@misc{wecalculate_cube_root_calculator, title = {Cube Root Calculator — ∛x Instantly}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cube-root-calculator}}, year = {2026}, note = {TG we-Calculate} }
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