Cube Calculator

What cubing means

Cubing a number means multiplying it by itself three times:

$x^3 = x \times x \times x$

For example, $5^3 = 5 \times 5 \times 5 = 125$. The small raised "3" is an exponent — cubing is the same as raising a number to the power of 3.

Why it's called "cubing": the volume connection

The name comes from geometry. A cube with side length $s$ has volume $s \times s \times s = s^3$ — every edge is the same length, so the volume calculation is literally "the side length, cubed." A storage box that is $5$ meters on each side has a volume of $5^3 = 125$ cubic meters.

The sign rule: cubing a negative number

Cubing behaves differently from squaring because 3 is an odd exponent. With squaring, the two negative signs always cancel. With cubing, there's a third factor left over that flips the result back to negative:

$(-3)^3 = (-3) \times (-3) \times (-3) = 9 \times (-3) = -27$

The first two factors multiply to a positive $9$ (a negative times a negative), but that $9$ is then multiplied by the third $-3$, flipping the sign back to negative. So $(-3)^3 = -27$, staying negative — the opposite of $(-3)^2 = 9$, which stays positive.

This calculator always reads a negative number typed into the field as the whole value being cubed. Entering $-3$ computes $(-3)^3 = -27$, the same way a graphing calculator treats a parenthesized negative base.

Cubing always keeps the sign of x

For any real number $x$:

$x^3 \text{ has the same sign as } x$

If $x > 0$, then $x^3 > 0$. If $x < 0$, then $x^3 < 0$. And $0^3 = 0$. This is different from squaring, where the result is always non-negative regardless of x's sign — cubing is the simplest example of an odd power, and every odd power preserves sign the same way.

Decimal cubes, computed exactly

The number being cubed doesn't need to be a whole number: $2.5^3 = 2.5 \times 2.5 \times 2.5 = 15.625$. This calculator computes decimal cubes with exact decimal arithmetic (not floating-point multiplication), so a value like $2.5^3$ comes out exactly $15.625$, rather than showing tiny binary-rounding artifacts.

The inverse: cube root

Cubing and taking a cube root undo each other. If $x^3 = y$, then $x = \sqrt[3]{y}$. Unlike square roots, cube roots don't have this ambiguity problem: because cubing preserves sign, every real number has exactly one real cube root — $5^3 = 125$ means $\sqrt[3]{125} = 5$, and $(-3)^3 = -27$ means $\sqrt[3]{-27} = -3$. For the reverse operation — finding $\sqrt[3]{y}$ from $y$ — use the Cube Root calculator.

Worked examples

Example 1 — positive integer: $5^3 = 5 \times 5 \times 5 = 125$.

Example 2 — negative integer: $(-3)^3 = (-3) \times (-3) \times (-3) = -27$ — negative, because cubing is an odd power.

Example 3 — decimal: $2.5^3 = 2.5 \times 2.5 \times 2.5 = 15.625$.

Example 4 — zero: $0^3 = 0 \times 0 \times 0 = 0$.

Where cubing shows up

Cubing appears throughout math and science: the volume formulas for cubes and spheres ($\frac{4}{3}\pi r^3$), density calculations (mass per cubic unit), and cubic equations in algebra. Cubing is the special case of the Exponents calculator where the exponent is fixed at 3 — squaring (exponent 2) is the other common special case, with its own dedicated Square calculator.