Direct answer

What are the main rectangle formulas?

The main rectangle formulas are area $A = l w$ , perimeter $P = 2 (l + w)$ , and diagonal $d = l^{2} + w^{2}$ . Use length and width for area and perimeter; use the Pythagorean theorem to calculate the diagonal across the rectangle.

Short answer

Rectangle formulas at a glance

Area: $A = l w$ Perimeter: $P = 2 (l + w)$ Diagonal: $d = l^{2} + w^{2}$

Definition

What is a rectangle?

A rectangle is a 2D quadrilateral with four right angles and opposite sides equal.

Diagram

Rectangle diagram

Rectangle variables: length l, width w, and diagonal d.

Quick formula table

Rectangle Formulas quick table

Formula	Equation	Variables
Area	$A = l w$	l = length, w = width
Perimeter	$P = 2 (l + w)$	l = length, w = width
Diagonal	$d = l^{2} + w^{2}$	Pythagorean theorem

Formula explanation

How to use these formulas

Length and width are perpendicular sides. The diagonal is found by treating the rectangle as two right triangles.

Calculator

Rectangle Calculator

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

Examples

Step-by-step examples

Find area

Given l = 8 cm and w = 3 cm.
Use $A = l w$ .
$A = 8 \times 3 = 24 c m^{2}$ .

Find perimeter

Given l = 8 cm and w = 3 cm.
Use $P = 2 (l + w)$ .
$P = 2 (8 + 3) = 22 c m$ .

Find diagonal

Given l = 8 and w = 3.
Use $d = l^{2} + w^{2}$ .
$d = 73 \approx 8.54$ .

Find width from area

Given A = 45 in² and l = 9 in.
Use $w = A / l$ .
$w = 45/9 = 5 in$ .

Real-world rectangle problem

A garden is 12 ft by 7 ft.
Use $P = 2 (l + w)$ .
$P = 2 (12 + 7) = 38 f t o f e d g in g$ .

Reverse calculations

Solve backwards from known values

Task	Formula	When to use it
Find width from area	$w = A / l$	Use when area and length are known.
Find length from area	$l = A / w$	Use when area and width are known.
Find width from perimeter	$w = P /2 - l$	Use when perimeter and length are known.

Common mistakes

Adding length and width without doubling for perimeter.
Writing perimeter in square units.
Confusing length and width does not change area, but the units still matter.

Practice

Practice problems with answers

1. Find area when l = 11 cm and w = 4 cm.

$A = 44 c m^{2}$ .

2. Find perimeter when l = 11 cm and w = 4 cm.

$P = 2 (11 + 4) = 30 c m$ .

3. Find width when A = 72 ft² and l = 9 ft.

$w = 72/9 = 8 f t$ .

4. Find diagonal when l = 6 and w = 8.

$d = 36 + 64 = 10$ .

5. A poster is 18 in by 24 in. Find its area.

$A = 432 i n^{2}$ .

Related formulas

FAQ

Rectangle Formulas FAQ

What is the rectangle area formula?

The rectangle area formula is $A = l w$ .

What is the rectangle perimeter formula?

The perimeter formula is $P = 2 (l + w)$ .

How do you find the diagonal of a rectangle?

Use $d = l^{2} + w^{2}$ .