Cube Root Calculator
Free cube root calculator: get the decimal cube root of any number, check perfect cubes and see the simplified radical form like ∛54 = 3∛2.
About the Cube Root Calculator
The cube root of a number x is the value that multiplied by itself three times gives x: ∛x. This free cube root calculator returns the decimal cube root of any number — including negatives, since ∛(−64) = −4 — tells you whether the input is a perfect cube, and for integers factors out perfect cubes to show the simplified radical form, e.g. ∛54 = 3∛2.
Cube roots appear whenever volume is involved: side of a cube = ∛volume, radius from a sphere's volume, and scaling recipes or models in three dimensions. Students from middle school through engineering courses in Pakistan, India and beyond use them constantly. The calculator runs instantly in your browser and never shows NaN on invalid input — just a helpful hint.
How to Use the Cube Root Calculator
- 1Enter any number — positive, negative or decimal.
- 2Read the cube root to six decimal places.
- 3Check whether it is a perfect cube and view the simplified radical form for integers.
Frequently Asked Questions
How do I calculate a cube root by hand?
For perfect cubes, factor: 216 = 6 × 6 × 6 so ∛216 = 6. For others, estimate between known cubes — ∛50 lies between ∛27 = 3 and ∛64 = 4, closer to 4; refining gives 3.684. The calculator does this instantly to six decimals.
How is a cube root simplified into radical form?
Pull out perfect-cube factors: 54 = 27 × 2 = 3³ × 2, so ∛54 = 3∛2. Similarly ∛250 = ∛(125 × 2) = 5∛2. The calculator finds the largest perfect-cube factor automatically for integer inputs.
Can you take the cube root of a negative number?
Yes — unlike square roots, cube roots of negatives are real numbers because an odd number of negative factors stays negative: ∛(−64) = −4 since (−4)³ = −64. That is why this calculator accepts negative inputs.
What is the difference between a cube root and a square root?
A square root undoes squaring (two factors), a cube root undoes cubing (three factors): √64 = 8 but ∛64 = 4. Geometrically, square roots answer area questions and cube roots answer volume questions — a 125 cm³ cube has 5 cm sides because ∛125 = 5.