Cube Calculator (x³)
Calculate the cube of any positive or negative number (x³ = x × x × x) with scientific notation and step-by-step arithmetic.
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What Is a Cube Calculator (x³)?
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together: n³ = n × n × n.
How to Use This Calculator
- Enter any positive or negative real number.
- View the cubed result along with scientific notation.
- Review the step-by-step multiplication explanation.
Cube Power Formula
x^3 = x \times x \times x, \quad (-x)^3 = -x^3Unlike squares, cubing preserves the sign of the original number: positive cubed is positive, negative cubed is negative.
Worked Example
Scenario: Calculate the cube of -4
Given: x = -4
Operation: (-4)³ = (-4) × (-4) × (-4)
First multiplication: (-4) × (-4) = 16
Second multiplication: 16 × (-4) = -64
Tips & Key Notes
- Because an odd number of negatives produces a negative, (-x)³ = -(x³).
- Cubing numbers grows extremely quickly (e.g. 10³ = 1,000, 20³ = 8,000).
- Cubing is the inverse operation of finding the cube root (∛x).
Frequently Asked Questions
Why is it called "cubing"?
Because calculating the geometric volume of a three-dimensional cube with edge length s is s³: Volume = s³.
What are the first ten positive perfect cubes?
1, 8, 27, 64, 125, 216, 343, 512, 729, and 1,000.
Can the cube of a number be negative?
Yes. Any negative number cubed produces a negative result because negative × negative × negative = negative.
How do you cube a fraction?
Cube the numerator and denominator independently: (a/b)³ = a³ / b³.
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