โ Cube Root Calculator: Find the Cube Root of Any Number
By Shihab Mia ยท Updated 2026-07-05
The cube root of a number is the value that, multiplied by itself three times, gives that number.
This cube root calculator finds the cube root of any real number instantly, including negative numbers and decimals, where a negative input gives a negative answer. Type a value and you will see its cube root to up to six significant figures, whether the number is a perfect cube, and the value of that number cubed for reference. Everything runs in your browser using the exact same method a scientific calculator uses, so results are precise and private.
What is the Cube Root Calculator?
The cube root of a number is the value that, when multiplied by itself three times, produces the original number. Written with the radical symbol it looks like โ27 = 3, because 3 x 3 x 3 = 27. Cubing and taking a cube root are inverse operations: cubing 3 gives 27, and the cube root of 27 gives back 3. That is the single idea this whole tool rests on, and it is why a perfect cube like 8, 27 or 64 returns a clean whole number while most other inputs return a decimal.
Unlike a square root, the cube root of a negative number is a real number, and it is negative. The cube root of -8 is -2, because -2 x -2 x -2 = -8: two of the minus signs cancel and the third leaves the product negative. This matters in practice, because many calculators and even spreadsheet formulas that rely on raising a number to the power of one third will return an error or a complex value for negatives. This tool uses Math.cbrt under the hood, which is defined for the whole real number line, so a cube root of a negative number is handled correctly every time.
Most numbers are not perfect cubes, so their cube roots are irrational and never terminate. The cube root of 2 is about 1.25992, and the cube root of 10 is about 2.15443. We round the displayed answer to six significant figures and trim trailing zeros, which is enough precision for engineering, geometry and everyday maths while keeping the number readable. If you paste the result back in and cube it, you will get very close to the original value, with the tiny gap coming from that rounding rather than any error in the calculation.
The tool also tells you when your input is a perfect cube. It does this honestly: it rounds the computed cube root to the nearest whole number, cubes that whole number, and checks whether the result equals your input exactly. Only then does it label the number a perfect cube and show the clean integer. This avoids the classic floating point trap where a value that should be exactly 4 shows up as 3.9999999 and gets mislabelled. For non cubes, you simply get the accurate decimal.
Cube roots show up far more often than people expect. Any time you know a volume and want the length of a side, you are taking a cube root, because the volume of a cube is side cubed. They appear in scaling laws, in statistics through the standardised skewness measure, in finance when annualising a three period growth rate, and throughout physics and chemistry. Having a fast, reliable cube root of a number at hand removes the friction of reaching for a full scientific calculator or writing a formula.
When to use it
- Finding the side length of a cube or tank when you only know its volume, since side equals the cube root of the volume.
- Checking quickly whether a number is a perfect cube (like 125 or 343) for a maths class or a puzzle.
- Taking the cube root of a negative number, which many basic calculators refuse to do correctly.
- Reversing a cubed number to recover the original base during algebra or exam revision.
- Estimating a three period compound growth rate by taking the cube root of a total growth factor.
- Working with scaling and similarity problems in geometry, physics and engineering where lengths scale with the cube root of volume.
How to use the Cube Root Calculator
- Type or paste any real number into the input box (the default is 27).
- Read the cube root, shown to up to six significant figures, in the first result panel.
- Check the note beneath it to see whether your number is a perfect cube.
- Use the second panel to see n cubed as a quick reference for the reverse operation.
- Try a negative value such as -8 to confirm the cube root comes out negative.
- Press Copy cube root to place the answer on your clipboard.
Formula & method
Worked examples
Find the cube root of 64 and confirm it is a perfect cube.
- Ask which number times itself three times gives 64.
- Test 4: 4 x 4 = 16, then 16 x 4 = 64.
- Since 4 is a whole number, 64 is a perfect cube.
- Round(4) cubed is 4 x 4 x 4 = 64, which equals the input exactly.
Result: The cube root of 64 is 4, and 64 is a perfect cube.
Find the cube root of -8 (a negative number).
- A cube root can be negative, so look for a negative candidate.
- Test -2: -2 x -2 = 4 (two negatives cancel).
- Then 4 x -2 = -8, matching the input.
- So the cube root of -8 is -2, and -8 is a perfect cube.
Result: The cube root of -8 is -2.
Find the cube root of 20 (not a perfect cube).
- Bracket it: 2 cubed is 8 and 3 cubed is 27, so the answer is between 2 and 3.
- It is closer to 27 than 8, so estimate near 2.7.
- The calculator returns 2.71442 to six significant figures.
- Cube it back: 2.71442 cubed is about 20.0000, confirming the value.
Result: The cube root of 20 is approximately 2.71442.
Perfect cubes and their cube roots
| Cube root (n) | Number (n cubed) |
|---|---|
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1,000 |
Cube roots of numbers that are not perfect cubes (rounded to 5 decimals)
| Number | Cube root |
|---|---|
| 2 | 1.25992 |
| 5 | 1.70998 |
| 10 | 2.15443 |
| 20 | 2.71442 |
| 50 | 3.68403 |
| 100 | 4.64159 |
Cube roots of negative numbers (the answer is negative)
| Number | Cube root |
|---|---|
| -1 | -1 |
| -8 | -2 |
| -27 | -3 |
| -64 | -4 |
| -125 | -5 |
Common mistakes to avoid
- Thinking a cube root of a negative number has no real answer. That rule is for square roots. A cube root of a negative number is a real, negative number: the cube root of -27 is -3, because -3 multiplied by itself three times gives -27.
- Confusing the cube root with dividing by three. The cube root of 27 is 3, not 9. Taking a cube root is not division; it is the inverse of cubing. โ27 asks what number cubed gives 27, and that is 3.
- Mixing up n cubed and the cube root of n. Cubing makes numbers bigger for values above 1, while the cube root makes them smaller. 4 cubed is 64, but the cube root of 4 is only about 1.5874. This tool shows both so you can see the difference at a glance.
- Trusting a floating point result that looks slightly off. Raising a number to the power 1/3 in code can produce 3.9999999 instead of 4. This calculator checks for a perfect cube by rounding and cubing back, so it reports a clean 4 when the input truly is a perfect cube.
- Assuming the cube root of a decimal below 1 stays below 1. It does, but it moves toward 1, not toward 0. The cube root of 0.125 is 0.5, which is larger than 0.125. Small positive numbers get pulled up toward 1 by a cube root.
Glossary
- Cube root
- The value that, multiplied by itself three times, gives the original number; written with the radical symbol as โ n.
- Cube (cubed number)
- The result of multiplying a number by itself three times, written n cubed or n to the power 3.
- Perfect cube
- A number whose cube root is a whole number, such as 8, 27, 64 or 125.
- Radical symbol
- The sign used to write roots; โ with a small 3 means a cube root.
- Radicand
- The number sitting under the radical symbol, that is the number whose root you are taking.
- Nth root
- A generalisation of square and cube roots; the nth root of a number is the value raised to the power n to get that number.
- Irrational number
- A number whose decimal expansion never ends or repeats, which is what most cube roots are.
- Significant figures
- The meaningful digits in a number; this tool rounds cube roots to six significant figures.
Frequently asked questions
What is a cube root calculator?
A cube root calculator finds the value that, when multiplied by itself three times, equals the number you enter. Type any real number and it returns the cube root to six significant figures, tells you whether the number is a perfect cube, and shows that number cubed for reference.
How do you find the cube root of a number?
To find the cube root of a number, look for the value whose cube equals it. For perfect cubes you can recall them (โ27 = 3, โ64 = 4). For other numbers you bracket the answer between two known cubes and refine, or simply let this calculator compute it exactly using Math.cbrt.
Can you take the cube root of a negative number?
Yes. The cube root of a negative number is real and negative. For example the cube root of -8 is -2, because -2 x -2 x -2 = -8. This is different from a square root, which has no real value for negatives.
What is a perfect cube?
A perfect cube is a number whose cube root is a whole number, such as 1, 8, 27, 64, 125 and 216. This tool flags a perfect cube by rounding the cube root, cubing it back, and confirming it exactly matches your input.
What is the difference between a cube root and squaring or square roots?
A square root undoes squaring (two equal factors) and does not exist as a real number for negatives, while a cube root undoes cubing (three equal factors) and works fine for negatives. The cube root of 64 is 4, whereas the square root of 64 is 8.
What is the cube root of 2?
The cube root of 2 is approximately 1.25992. It is an irrational number, so its decimal never ends or repeats; this calculator shows it rounded to six significant figures.
How do I find the cube root without a calculator?
Bracket the number between two perfect cubes you know, then estimate. For the cube root of 20, note that 2 cubed is 8 and 3 cubed is 27, so the answer sits between 2 and 3 and closer to 3, around 2.71. For an exact value, use this cube root calculator.
How is the cube root related to volume?
The volume of a cube is its side length cubed, so the side length is the cube root of the volume. If a cube shaped tank holds 1,000 cubic units, each side is โ1000 = 10 units. This is one of the most common real uses of a cube root.
What is the cube root of a decimal like 0.125?
The cube root of 0.125 is 0.5, because 0.5 x 0.5 x 0.5 = 0.125. Notice the cube root of a small positive decimal is larger than the decimal itself, moving toward 1.
Is this cube root calculator free and private?
Yes. It is completely free, needs no sign up, and runs entirely in your browser. Nothing you type is sent to a server, so your numbers stay on your device.