Home › Math & Science › Cube Root Calculator
Cube Root Calculator
Use this free cube root calculator to find the cube root of any number — positive, negative, whole or decimal. Type the number and press the button: perfect cubes like 729 return their exact whole-number root, and everything else is worked out to six decimal places. A full table of cubes from 1 to 20 is included below for quick lookups and homework checks.
| Root type | Perfect cube — exact root |
| Check: root cubed | 9³ = 729 |
How to use this calculator
- Type the number whose cube root you want. Negative numbers are welcome.
- Press Find cube root.
- If the number is a perfect cube, the result is an exact whole number and the check line proves it by cubing the root.
- If it is not a perfect cube, the root is shown to six decimal places.
- Use the table below when you just need a common cube quickly.
How cube roots work
Cubing a number means multiplying it by itself three times: 4 cubed is 4 × 4 × 4 = 64. The cube root runs the process backwards:
Unlike square roots, cube roots work for every real number, because three negatives multiply to a negative: (−3)³ = −27, so ∛(−27) = −3. The table lists the first twenty perfect cubes — learn to spot them and most textbook cube roots become instant.
| Number (n) | Cube (n³) | Number (n) | Cube (n³) |
|---|---|---|---|
| 1 | 1 | 11 | 1331 |
| 2 | 8 | 12 | 1728 |
| 3 | 27 | 13 | 2197 |
| 4 | 64 | 14 | 2744 |
| 5 | 125 | 15 | 3375 |
| 6 | 216 | 16 | 4096 |
| 7 | 343 | 17 | 4913 |
| 8 | 512 | 18 | 5832 |
| 9 | 729 | 19 | 6859 |
| 10 | 1000 | 20 | 8000 |
Worked example
Find the cube root of 729.
Step 1: look for it in the cubes table — 729 appears as 9³.
Step 2: so the cube root is 9.
Step 3: verify by cubing — 9 × 9 = 81, and 81 × 9 = 729. Exact.
Now a non-perfect case: the cube root of 100 lies between ∛64 (4) and ∛125 (5), and the calculator gives 4.641589. Cubing 4.641589 returns 100.000 — the tiny difference from 100 is only the rounding of the last decimal place. The calculator opens with 729 entered, so its first answer matches the main example.
FAQ
What is a cube root?
The cube root of a number is the value that, multiplied by itself three times, gives the number back. The cube root of 729 is 9 because 9 times 9 times 9 is 729. It is the reverse of cubing, just as the square root is the reverse of squaring. Cube roots appear wherever volumes are involved: if you know a cube-shaped tank holds 729 litres, its side is the cube root of 729 — 9 units — long.
What is the cube root of 729?
The cube root of 729 is exactly 9. You can check it by multiplying: 9 cubed is 9 times 9 (81) times 9, which is 729. 729 is a perfect cube — in fact it is both 9 cubed and 27 squared — so its cube root is a whole number with no decimal part. This calculator detects perfect cubes like this and shows the exact integer instead of a rounded decimal.
Can a cube root be negative?
Yes — and this is the big difference from square roots. Multiplying three negative numbers gives a negative result, so every negative number has a real cube root: the cube root of minus 27 is minus 3, because minus 3 cubed is minus 27. Square roots of negatives are not real numbers, but cube roots always are. Enter a negative number in this calculator and it returns the negative root directly.
How can I estimate a cube root without a calculator?
Bracket it between two perfect cubes you know. The cube root of 100, for example, lies between the cube root of 64 (4) and the cube root of 125 (5). Since 100 is closer to 125 than to 64 — a bit over two-thirds of the way — the answer is about 4.6 to 4.7; the exact value is 4.641589. Prime factorisation gives exact answers for perfect cubes: group the factors in threes and take one from each group.
What are the first perfect cubes?
Cubing 1 to 10 gives 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000. These are worth recognising on sight, because any cube root that lands exactly on a whole number must be one of this family. The table on this page runs to 20 cubed, which is 8000. If your number sits between two entries, its cube root is a decimal between the two matching roots — this calculator shows it to six decimal places.
What are the cube roots of 0 and 1?
Both are themselves: the cube root of 0 is 0, because 0 cubed is 0, and the cube root of 1 is 1, because 1 cubed is 1. The same holds for minus 1 — its cube root is minus 1. These fixed points are handy sanity checks: any method or calculator that does not return 0, 1 and minus 1 for these three inputs is doing something wrong.