Cube Calculator
Calculate the cube of any number instantly. Free online cube calculator (x3) with step-by-step multiplication.
What is a Cube of a Number?
The cube of a number is the result of multiplying the number by itself three times. It is written as $$x^3$$ and pronounced as "x cubed" or "x to the third power." The formula is simple: $$x^3 = x \times x \times x$$.
For example, $$4^3 = 4 \times 4 \times 4 = 64$$. This means that 4 cubed equals 64. Cubing a number is a fundamental operation in mathematics, used in geometry (volume of a cube), physics, engineering, and many other fields.
How to Use the Cube Calculator
Enter any real number into the calculator. The tool instantly computes the cube using the formula $$x^3 = x \times x \times x$$. It shows the step-by-step multiplication process, making it easy to understand how the result is derived. The calculator supports positive numbers, negative numbers, decimals, and scientific notation.
$$x^3 = x \times x \times x$$
Perfect Cubes
A perfect cube results when you cube an integer (a whole number without decimals or fractions). For example, $$3^3 = 27$$, so 27 is a perfect cube. Perfect cubes have the property that their cube root is an integer.
| n | n³ | Perfect Cube |
|---|---|---|
| 0 | 0 | 0 × 0 × 0 |
| 1 | 1 | 1 × 1 × 1 |
| 2 | 8 | 2 × 2 × 2 |
| 3 | 27 | 3 × 3 × 3 |
| 4 | 64 | 4 × 4 × 4 |
| 5 | 125 | 5 × 5 × 5 |
| 6 | 216 | 6 × 6 × 6 |
| 7 | 343 | 7 × 7 × 7 |
| 8 | 512 | 8 × 8 × 8 |
| 9 | 729 | 9 × 9 × 9 |
| 10 | 1000 | 10 × 10 × 10 |
Cubing Negative Numbers
When you cube a negative number, the result is always negative. This is because multiplying an odd number of negatives results in a negative number. For example:
- $$(-2)^3 = (-2) \times (-2) \times (-2) = -8$$
- $$(-5)^3 = (-5) \times (-5) \times (-5) = -125$$
Be careful with parentheses when using the calculator. $$-2^3$$ means the negative of $$2^3$$, which equals -8, just like $$(-2)^3$$. This is because the exponent applies before the negation.
Applications of Cubes
- Volume: The volume of a cube with side length s is $$V = s^3$$.
- Physics: Cubic relationships appear in inverse-square law calculations, fluid dynamics, and density calculations.
- Engineering: Material strength calculations often involve cubic relationships.
- Data Storage: Memory sizes are often measured in cubic capacities (KB, MB, GB).
- Computer Graphics: 3D rendering uses cubic Bezier curves and volumetric calculations.
Frequently Asked Questions
Frequently Asked Questions
What does x cubed mean?
X cubed (written as $$x^3$$) means x multiplied by itself three times: $$x \times x \times x$$. The exponent 3 indicates that the base number should be used as a factor three times.
What is a perfect cube?
A perfect cube is the result of cubing an integer. For example, 8 is a perfect cube because $$2^3 = 8$$. Other examples include 1, 27, 64, 125, 216, 343, 512, 729, and 1000.
What is 3 cubed?
3 cubed (written as $$3^3$$) equals 27. This is calculated as $$3 \times 3 \times 3 = 27$$. Since 3 is an integer, 27 is a perfect cube.
Is a negative number cubed still negative?
Yes, when you cube a negative number, the result is always negative. For example, $$(-3)^3 = -27$$. This is because an odd number of negative multiplications yields a negative result.
What is the difference between square and cube?
A square ($$x^2$$) multiplies a number by itself once: $$x \times x$$. A cube ($$x^3$$) multiplies a number by itself twice: $$x \times x \times x$$. A square of a negative number is always positive, while a cube of a negative number is always negative.
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