Cube Root Calculator
Calculate the cube root of any real number. Shows exact result for perfect cubes, decimal approximation for others, and the verification check.
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How to use this calculator
The cube root of x is the number y such that y³ = x. Unlike square roots, cube roots of negative numbers are real (e.g., ∛(−8) = −2).
- 1
Enter any real number — positive, negative, or zero.
- 2
The cube root is calculated immediately. Negative inputs give negative cube roots.
- 3
If the input is a perfect cube (like 8, 27, 64), the exact integer result is confirmed.
- 4
The verification row shows cbrt³ rounded back, confirming accuracy.
Frequently asked questions
Can a negative number have a cube root?
Yes. Cubing preserves sign, so (−4)³ = −64 and the real cube root of −64 is −4. The calculator returns −4 for −64 and −1.25992105 for −2. Unlike square roots, no imaginary numbers are needed for negative inputs. A cube root also has two complex cousins, which this tool does not show.
How does the “Perfect cube?” check work?
It rounds the root to about twelve significant digits and cubes it back. If that equals your input within a tiny relative tolerance, it says “Yes” and prints the root. This works for decimals too: 0.001 is reported as a perfect cube with root 0.1, and 0.125 with root 0.5. Everything else is reported as “No (irrational)”.
Why is the displayed cube root not exactly right for a non-perfect cube?
The roots of non-cubes such as 2 and 100 are irrational, so their decimal expansions never end. The result is rounded to 8 decimals: ∛2 = 1.25992105 and ∛100 = 4.64158883. The “Verification” row cubes the unrounded value and shows the input back.
Why does x^(1/3) on some calculators fail for negatives?
Raising a negative base to a fractional power is not defined for real numbers in many calculators and programs, which return an error or NaN. This tool takes the real cube root directly, which is why −64 gives −4. The exponent-form row writes negative inputs in brackets, such as (−64)^(1/3), to make clear the whole number is the base.
What does it do with zero?
It returns 0 and calls it a perfect cube, since 0³ = 0. Clearing the box counts as 0, so an emptied field also returns 0 and the perfect-cube message.
How large or small can the input be?
Normal double-precision numbers work, including scientific notation. 1e27 returns 1,000,000,000 and is recognised as a perfect cube. The “perfect cube” detection is meant for typed decimals; extremely long integers can be rounded by the floating-point format before the tool sees them.
Can I find the side of a cube from its volume?
Yes: the edge length is the cube root of the volume. A cube holding 1,000 cubic units has an edge of 10, and 2.5 cubic units gives an edge of 1.35720881. Units are cubic for the input and linear for the answer.
Does it compute other roots or powers?
No. It handles cube roots only. For other orders use a general nth-root or exponent calculator.
Cube root calculator — real roots of any number
What a cube root is
The cube root of x is the number y with y × y × y = x, written ∛x or x^(1/3). Every real number has exactly one real cube root, and it has the same sign as x. Perfect cubes of integers give whole-number answers; everything else gives an irrational decimal. The calculator shows the root, whether the input is a perfect cube, the verification (root cubed) and the exponent form.
Worked examples
Perfect cubes return a whole number and are marked as such, while other inputs return a decimal approximation. Negative inputs work too, because a real cube root of a negative number is negative. Each row below is a direct result from the calculator.
| Input x | ∛x | Perfect cube? |
|---|---|---|
| 27 | 3 | Yes |
| −64 | −4 | Yes |
| 0.001 | 0.1 | Yes |
| 0.125 | 0.5 | Yes |
| 2 | 1.25992105 | No |
| 10 | 2.15443469 | No |
| 100 | 4.64158883 | No |
| −2 | −1.25992105 | No |
Cube sizes and volumes
The most common practical use is turning a volume into an edge length. A cubic container of volume 1,000 has sides of 10 in the matching unit, and one of 2.5 cubic units has sides of 1.35720881. Since volumes scale with the cube of length, doubling the edge multiplies the volume by 8; going the other way, a container needing twice the volume has an edge only ∛2 ≈ 1.26 times longer. To scale a volume by a factor k, scale lengths by ∛k.
Perfect cubes to recognise
The first positive perfect cubes are 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1,000. Their negatives work equally well, as with −64 giving −4. Decimals that are cubes of terminating decimals also count: 0.001 is 0.1 cubed and 0.125 is 0.5 cubed. If the tool says a number is not a perfect cube, its root is irrational and will always be shown as a rounded decimal.
Checking and precision
Cubing the displayed root will not reproduce the input exactly for non-perfect cubes, because the root is rounded to 8 decimals. The verification row uses the full-precision value internally, so it normally shows the original number. If you need exact radical form, such as 2∛3 for ∛24, simplify by hand; this tool returns decimals only. Non-numeric entries return an error prompt, and the root is computed in ordinary double precision.
Learn more from an authoritative source:
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →