Direct answer

What are the main square formulas?

The main square formulas are area $A = s^{2}$ , perimeter $P = 4 s$ , and diagonal $d = s 2$ . A square has four equal sides, so one side length is enough to calculate its area, perimeter, and diagonal. Use square units for area and linear units for perimeter and diagonal.

Short answer

Square formulas at a glance

Area: $A = s^{2}$ Perimeter: $P = 4 s$ Diagonal: $d = s 2$

Definition

What is a square?

A square is a 2D shape with four equal sides and four right angles.

Diagram

Square diagram

Square variables: side length s and diagonal d.

Quick formula table

Square Formulas quick table

Formula	Equation	Variables
Area	$A = s^{2}$	s = side length
Perimeter	$P = 4 s$	s = side length
Diagonal	$d = s 2$	s = side length

Formula explanation

How to use these formulas

A square is a rectangle where length and width are the same, so all formulas can be written using one side length.

Calculator

Square Calculator

Enter measurements to get the result, unit, formula, and calculation steps.

Examples

Step-by-step examples

Find area

Given s = 9 cm.
Use $A = s^{2}$ .
$A = 9^{2} = 81 c m^{2}$ .

Find perimeter

Given s = 9 cm.
Use $P = 4 s$ .
$P = 4 \times 9 = 36 c m$ .

Find diagonal

Given s = 9 cm.
Use $d = s 2$ .
$d = 92 \approx 12.73 c m$ .

Find side from area

Given A = 64 cm².
Use $s = A$ .
$s = 64 = 8 c m$ .

Find side from perimeter

Given P = 52 m.
Use $s = P /4$ .
$s = 52/4 = 13 m$ .

Reverse calculations

Solve backwards from known values

Task	Formula	When to use it
Find side from area	$s = A$	Use when area is known.
Find side from perimeter	$s = P /4$	Use when perimeter is known.
Find side from diagonal	$s = d / 2$	Use when diagonal is known.

Common mistakes

Multiplying by 4 for area instead of squaring the side.
Using square units for perimeter.
Forgetting that the diagonal is longer than a side.

Practice

Practice problems with answers

1. Find area when s = 12 cm.

$A = 144 c m^{2}$ .

2. Find perimeter when s = 12 cm.

$P = 48 c m$ .

3. Find side when A = 81 m².

$s = 81 = 9 m$ .

4. Find diagonal when s = 10 in.

$d = 102 \approx 14.14 in$ .

5. Find side when perimeter is 100 ft.

$s = 100/4 = 25 f t$ .

Related formulas

FAQ

Square Formulas FAQ

What is the square area formula?

The area formula is $A = s^{2}$ .

What is the square perimeter formula?

The perimeter formula is $P = 4 s$ .

What is the diagonal of a square?

The diagonal is $d = s 2$ .