Exponent Calculator · Practical guide
How to Find the Cube Root of a Number
The cube root of x is the number that, cubed, gives x back — cube root of 27 = 3 and cube root of 2 is about 1.2599.
At a glance
What a Cube Root Means
The cube root of a number x, written x^(1/3), is the value that multiplied by itself three times returns x. Since 3 x 3 x 3 = 27, the cube root of 27 is 3. For numbers that are not perfect cubes, the result is a decimal: the cube root of 2 ≈ 1.259921, because 1.259921^3 ≈ 2.
Interactive tool
Exponent Calculator
Enter your own values, then compare the result with the examples below.
Results
Perfect Cubes Worth Memorizing
| Number | Cube Root | Number | Cube Root |
|---|---|---|---|
| 1 | 1 | 216 | 6 |
| 8 | 2 | 343 | 7 |
| 27 | 3 | 512 | 8 |
| 64 | 4 | 729 | 9 |
| 125 | 5 | 1,000 | 10 |
Estimating Between Perfect Cubes
Bracket the number between two cubes you know. The cube root of 50 sits between 3 (27) and 4 (64), and since 50 is closer to 64, the answer should be near 3.7 — the exact value is about 3.684031. This bracketing trick lets you sanity-check any calculator result instantly.
Cube Roots of Negative Numbers
Unlike square roots, cube roots of negatives are perfectly real: the cube root of -8 is -2, because (-2)^3 = -8. The calculator above handles this through the root operation with degree 3 — odd roots of negative numbers work, while even roots of negatives are not real.
Beyond Cube Roots
The same idea generalizes: the fourth root of 81 is 3 (3^4 = 81) and the fifth root of 32 is 2. Enter any degree in the root operation to compute n-th roots directly.
Frequently Asked Questions
Is there a cube root button on this calculator?
Use the Root operation: enter your number as the base and 3 as the degree. The result is the same as raising the number to the 1/3 power.
Why can cube roots handle negatives when square roots cannot?
A negative number times itself three times stays negative, so every negative number has a real cube root. Squaring a negative gives a positive, so no real number squares to a negative.
How is the cube root used in real life?
Cube roots reverse volume problems: if a cube-shaped tank holds 500 gallons (about 66.8 cubic feet), its side length is the cube root of 66.8, about 4.06 feet.
Is the cube root of 1/8 a fraction?
Yes. The cube root of 1/8 is 1/2 = 0.5, because (1/2)^3 = 1/8. Cube roots of fractions take the cube root of the numerator and denominator separately.