Square Calculator

What squaring means

Squaring a number means multiplying it by itself:

$x^2 = x \times x$

For example, $12^2 = 12 \times 12 = 144$. The small raised "2" is an exponent — squaring is the same as raising a number to the power of 2.

Why it's called "squaring": the area connection

The name comes from geometry. A square with side length $s$ has area $s \times s = s^2$ — every side is the same length, so the area calculation is literally "the side length, squared." A garden bed that is $12$ meters on each side has an area of $12^2 = 144$ square meters.

The sign trap: $-7^2$ vs. $(-7)^2$

This is one of the most common mistakes in algebra, because the two expressions look almost identical but mean different things:

Without parentheses, the exponent applies only to the $7$, and the minus sign is applied after squaring — so $-7^2 = -(7^2) = -49$. With parentheses, the minus sign is part of the number being squared, so $(-7)^2 = (-7) \times (-7) = 49$.

This calculator always reads a negative number typed into the field as the whole value being squared. Entering $-7$ computes $(-7)^2 = 49$, the same way a graphing calculator treats a parenthesized negative base.

Squaring is always non-negative

For any real number $x$:

$x^2 \geq 0$

The smallest possible square is $0^2 = 0$. Every other square — whether $x$ is positive or negative — is strictly positive. This is why $x^2 = -9$ has no real solution: no real number, positive or negative, squares to a negative value.

Decimal squares, computed exactly

The number being squared doesn't need to be a whole number: $2.5^2 = 2.5 \times 2.5 = 6.25$. This calculator computes decimal squares with exact decimal arithmetic (not floating-point multiplication), so a value like $0.29^2 = 0.0841$ comes out precise, rather than showing tiny binary-rounding artifacts like $0.08409999999999999$.

The inverse: square root

Squaring and taking a square root undo each other. If $x^2 = y$, then $x = \sqrt{y}$ (taking the non-negative root). Because squaring always produces a non-negative result, every positive number has two square roots: $7^2 = 49$ and $(-7)^2 = 49$, so both $7$ and $-7$ are square roots of $49$. For the reverse operation — finding $\sqrt{y}$ from $y$ — use the Square Root calculator.

Worked examples

Example 1 — positive integer: $12^2 = 12 \times 12 = 144$.

Example 2 — negative integer: $(-7)^2 = (-7) \times (-7) = 49$ — positive, because the sign cancels.

Example 3 — decimal: $2.5^2 = 2.5 \times 2.5 = 6.25$.

Example 4 — zero: $0^2 = 0 \times 0 = 0$.

Where squaring shows up

Squaring appears throughout math and science: the area formulas for squares and circles ($\pi r^2$), the Pythagorean theorem ($a^2 + b^2 = c^2$), variance and standard deviation in statistics, and the inverse-square laws in physics (gravity, light intensity). Squaring is the special case of the Exponents calculator where the exponent is fixed at 2 — cubing (exponent 3) is the next most common special case, with its own dedicated Cube calculator.