Cube Root Calculator
Compute ∛n for any real number, including negative inputs.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this cube root calculator
- Enter any real number in the Number field — negatives are allowed.
- Press Calculate to see the cube root.
- Read whether the input is a perfect cube in the explanatory line.
- Use Copy to put the result on your clipboard, or Reset to clear the input.
About this cube root calculator
The cube root calculator returns the real cube root of any number, including negatives. Unlike square roots, every real number has exactly one real cube root, because raising a negative real number to an odd power preserves the sign. The tool also flags whether the input is a perfect cube — i.e. whether the result is a whole integer.
The cube root of n is defined as the real number r such that r × r × r = n. For perfect cubes the result is exact: ∛27 = 3 because 3 × 3 × 3 = 27, and ∛−8 = −2 because (−2) × (−2) × (−2) = −8. For non-perfect cubes the result is an irrational decimal approximation, shown to up to ten places: ∛10 ≈ 2.1544346900. The calculation uses JavaScript's built-in Math.cbrt, which is accurate to standard IEEE-754 double precision.
Use cases include geometry (finding side length from a cube's volume), physics, and engineering problems involving inverse cubic relationships.
FAQ
- What does the cube root calculator do?
- It computes the real cube root of any number, positive or negative, and tells you whether the input is a perfect cube.
- What formula does it use?
- The cube root of n is the real number r such that r × r × r = n. The tool uses JavaScript's Math.cbrt, which preserves sign for negative inputs.
- Why does cube root accept negative numbers when square root does not?
- Raising a negative real to an odd power keeps the sign negative, so every real number has exactly one real cube root. Squaring a real number always gives a non-negative result, so negatives have no real square root.
- How accurate is the result?
- Perfect cubes return exact integers. Other numbers are correct to about 15–16 significant digits, displayed up to 10 decimal places.
- Does this tool store my numbers?
- No. The calculation runs entirely in your browser; nothing is sent to a server or saved between visits.
- Is the cube root calculator free?
- Yes. It is free to use with no signup, no account, and no usage limit.