About the Cube Root Calculator
The cube root of a number is the value that gives the number when multiplied by itself three times. The cube root of 27 is 3, because 3 × 3 × 3 = 27. Unlike square roots, cube roots exist for negative numbers: the cube root of −8 is −2. This calculator finds cube roots and also any other root from the square root up to the thousandth root. It tells you when the number is a perfect power, so the root is a whole number, and checks the answer by raising it back to the power. It is useful for volume problems, scaling, physics and school maths.
Updated October 2026
How to use the Cube Root Calculator
- 1Type the number.
- 2Leave the root at 3 for a cube root, or change it for a square root, fourth root and so on.
- 3Read the root and whether it is a perfect power.
- 4Check the verification line.
- 5See the rounded values for use in your work.
Perfect cubes to remember
- 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64.
- 5³ = 125, 6³ = 216, 7³ = 343.
- 8³ = 512, 9³ = 729, 10³ = 1,000.
- 11³ = 1,331, 12³ = 1,728.
- 20³ = 8,000, 100³ = 1,000,000.
Estimating by hand
To estimate the cube root of 100, note that 4³ = 64 and 5³ = 125, so the answer is between 4 and 5, closer to 5. Try 4.6: 4.6³ is 97.3. Try 4.65: 100.5. So the cube root of 100 is about 4.64. The calculator confirms 4.6416, and a couple of guesses like this show how the number behaves.
A word of warning for calculators and spreadsheets: raising a negative number to the power one third often fails or gives a complex number, because the power function is defined for positive bases only. That is why this tool handles the sign separately, taking the cube root of the positive version and putting the minus sign back on afterwards. In a spreadsheet, you can do the same with a formula that multiplies the sign of the number by the cube root of its absolute value.
Real-world uses
Cube roots appear in scaling laws: if you double the linear size of an object, its volume goes up eightfold, so to halve a volume you shrink each side by the cube root of 2, about 0.794. They also show up in physics formulas, in engineering for sizing shafts and in statistics for transforming data that is skewed.
Related tools
The Square Root Calculator and Exponent Calculator are close relatives, the Volume Calculator turns sides into volume, the Sphere Calculator uses cube roots to find radius from volume and the Scientific Calculator handles longer expressions.
Features
- Cube root, square root and any nth root
- Negative numbers for odd roots
- Perfect power detection
- Verification by raising back
- Rounded values
- Clear message for impossible roots
Frequently asked questions
How do I find the cube root of a number?
Find the number which multiplied by itself three times gives the original. For non-perfect cubes, use this calculator or estimate between two perfect cubes. The cube root of 50 lies between 3 (27) and 4 (64), at about 3.684.
What is the cube root of 27?
3, since 3³ = 27. The cube roots of 8, 64, 125 and 1,000 are 2, 4, 5 and 10.
Can you take the cube root of a negative number?
Yes. A negative number multiplied by itself three times stays negative, so the cube root of −27 is −3. Even roots, such as the square root, of negative numbers are not real.
What is a perfect cube?
A whole number that is the cube of a whole number: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000 and so on. The tool tells you when your number is one.
How do I find other roots?
Change the Root box. 2 gives the square root, 4 the fourth root, and so on. The nth root of x is the same as x raised to the power 1/n.
Why is the cube root used in volume problems?
If you know the volume of a cube, its side length is the cube root of the volume. A cubic tank holding 64 litres has sides of 4 decimetres, or 40 centimetres.