The cube of a number is that number multiplied by itself three times, written x³ and read “x cubed.” Cubes measure volume, appear in physical laws such as the inverse-cube behavior of some forces, and grow far faster than squares. This calculator cubes any number exactly, whether it is a whole number with many digits, a decimal, a negative number or a fraction.
How to use the cube number calculator
- Type the number into Number (x). Whole numbers of any length, decimals like 2.5, negatives and fractions such as 2/3 all work.
- Read x³ on the tape, together with its digit count and, for large values, scientific notation.
- Open the steps to see the repeated multiplication, the place-value shortcut for two- to four-digit whole numbers, or the decimal-place rule.
The cube formula
Expanding a sum gives a handy mental-math identity:
Worked example: 12³
Direct: 12 × 12 = 144, and 144 × 12 = 1,728.
Shortcut: split 12 into 10 + 2. Then 10³ = 1,000, 3 × 10² × 2 = 600, 3 × 10 × 2² = 120 and 2³ = 8. The total is 1,000 + 600 + 120 + 8 = 1,728.
Meaning: a box 12 inches on every side holds 1,728 cubic inches, which is exactly one cubic foot.
A negative example: (−47)³ = −103,823. The shortcut works on 47 (64,000 + 33,600 + 5,880 + 343), and the minus sign is put back at the end because an odd number of negative factors gives a negative product.
Cubes from 1 to 15
| n | n³ | n | n³ |
|---|---|---|---|
| 1 | 1 | 9 | 729 |
| 2 | 8 | 10 | 1,000 |
| 3 | 27 | 11 | 1,331 |
| 4 | 64 | 12 | 1,728 |
| 5 | 125 | 13 | 2,197 |
| 6 | 216 | 14 | 2,744 |
| 7 | 343 | 15 | 3,375 |
| 8 | 512 |
The list of perfect cubes extends this table as far as you like.
Interesting facts about cubes
- Last digits. Every digit 0–9 can end a cube, and the last digit of n³ identifies the last digit of n: a cube ending in 7 comes from a number ending in 3, and one ending in 8 comes from a number ending in 2.
- Sums of odd numbers. 1 = 1³, 3 + 5 = 2³, 7 + 9 + 11 = 3³, 13 + 15 + 17 + 19 = 4³. Each cube is a sum of consecutive odd numbers.
- Sum of cubes. 1³ + 2³ + … + n³ = (1 + 2 + … + n)². For n = 4: 1 + 8 + 27 + 64 = 100 = 10².
- The taxicab number. 1,729 = 1³ + 12³ = 9³ + 10³ is the smallest number that is a sum of two positive cubes in two different ways.
Cubes and units
When x has a unit, x³ has that unit cubed. A tank 2 m on each side holds 2³ = 8 m³, or 8,000 liters. Converting cubic units means cubing the conversion factor: 1 yd = 3 ft, so 1 yd³ = 27 ft³, a fact worth remembering when ordering concrete or mulch by the cubic yard.
To reverse a cube, use the cube root calculator. For full cube geometry, including surface area and diagonals, try the cube calculator.
Frequently asked questions
What does it mean to cube a number?
Cubing a number means using it as a factor three times: x³ = x × x × x. A cube with edge length x has a volume of x³ cubic units, which is where the name comes from.
Can a cube be negative?
Yes. Unlike squares, cubes keep the sign of the original number: (−4)³ = −64. Two negative factors make a positive, and the third makes the product negative again.
How do I cube a decimal?
Cube the digits without the decimal point and give the answer three times as many decimal places. For 2.5³, cube 25 to get 15,625; 2.5 has one decimal place, so the cube has three: 15.625.
How much bigger is a cube when its side doubles?
Eight times bigger, because 2³ = 8. Volume grows with the cube of the length, so a box twice as long, wide and tall holds eight times as much.