Cube Root Calculator
Find the cube root of any number, including negatives.
What the Cube Root Calculator does
Enter any number below to get its exact cube root instantly, along with the full step-by-step calculation. The cube root of a number is the value that, cubed, returns it. Unlike square roots, cube roots of negative numbers are perfectly real: the cube root of −27 is −3.
Formula
∛x = y where y³ = x
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Number | number | Yes | — |
How to use it
- Enter Number.
- Select Calculate.
Worked example
A cubic tank holds 343 litres. What is the edge length in decimetres?
- Number
- 343
∛343 = 7, so each edge is 7 dm.
Reading the result
- Every real number has exactly one real cube root. Cubing preserves sign, so the root keeps it too.
- Cube roots undo volume: a cube holding 27 cm³ has 3 cm sides.
Common mistakes
- Expecting a negative input to be rejected. Unlike a square root, the cube root of a negative number is a real number.
- Confusing the cube root with dividing by three. The cube root of 27 is 3, not 9.
Frequently asked questions
Why can cube roots handle negatives when square roots cannot?
A negative times a negative times a negative stays negative, so an odd root of a negative number exists. Even roots always produce a positive when multiplied out.
What is the cube root of 108000?
∛108000 ≈ 47.62. 108000 is not a perfect cube — 47³ = 103,823 and 48³ = 110,592 — so the result is a decimal rather than a whole number.
What is the cube root of 2375?
∛2375 ≈ 13.34. 2375 falls between 13³ = 2,197 and 14³ = 2,744, so its cube root is not exact.
How do you find a cube root without a calculator?
Bracket the number between two perfect cubes you already know, then narrow down. For 2375, 13³ = 2,197 and 14³ = 2,744, and 2375 sits closer to the lower one, giving ∛2375 ≈ 13.34. A perfect cube resolves exactly the same way: ∛−125 = −5, since (−5)³ = −125 — negative numbers work identically because an odd number of negative factors stays negative.