Area of a Rectangle Calculator

Enter length and width — instantly get area, perimeter, and diagonal with step-by-step working.

Unit:
Length (l)
cm
Width (w)
cm
Diagonal (d)
cm

💡 Enter any two values — the third and area update instantly.

Live Diagram

Rectangle Area Formulas

Area

A = l × w

Multiply length by width. The fundamental rectangle formula.

Perimeter

P = 2 × (l + w)

Sum both dimensions and double — the total boundary length.

Diagonal

d = √(l² + w²)

Pythagoras' theorem — the diagonal is the hypotenuse.

From Area & Length

w = A ÷ l

Rearrange A = l × w to find the missing dimension.

What Is a Rectangle?

A rectangle is a four-sided polygon (quadrilateral) with four right angles (90° each). Opposite sides are equal and parallel. It is the most common shape in everyday life — from rooms and screens to books and doors. A square is a special rectangle where all four sides are equal.

The area of a rectangle (A = l × w) represents the total surface enclosed. The diagonal of a rectangle creates two congruent right triangles, allowing Pythagoras' theorem to compute d = √(l² + w²). Unlike a square, a rectangle's diagonal depends on both dimensions.

l × w
Area — length times width
2(l+w)
Perimeter — sum of all sides
√(l²+w²)
Diagonal — by Pythagoras

How to Calculate the Area of a Rectangle

  1. 1

    Measure length and width

    Use the longer dimension as length (l) and the shorter as width (w). Both must be in the same unit.

  2. 2

    Multiply: A = l × w

    For l = 6 m, w = 4 m: A = 6 × 4 = 24 m². The result is in square units.

  3. 3

    Calculate perimeter if needed

    P = 2(l + w) = 2 × (6 + 4) = 2 × 10 = 20 m — the total boundary length.

  4. 4

    Find the diagonal (optional)

    d = √(l² + w²) = √(36 + 16) = √52 ≈ 7.21 m. Useful for checking squareness in construction.

Worked Example — Rectangular room 6 m × 4 m

Given: l = 6 m, w = 4 m
Area: A = 6 × 4 = 24 m²
Perim: P = 2 × (6 + 4) = 2 × 10 = 20 m
Diag: d = √(6² + 4²) = √(36 + 16) = √52 ≈ 7.21 m

Real-World Applications

🏠

Home

Room area for flooring, paint coverage, and carpet ordering. Perimeter determines skirting board length.

🖼️

Art & Photography

Canvas sizing, photo print area, and frame cost estimates all depend on rectangle area calculations.

📱

Technology

Screen dimensions, PCB board layouts, and display pixel density all involve rectangle area and diagonal calculations.

🌿

Garden & Landscaping

Lawn area for seeding or turf, vegetable patch sizing, and irrigation coverage use rectangle area formulas.

🏗️

Construction

Foundation layout, ceiling tile ordering, and wall surface area all require precise rectangle calculations for cost planning.

📋

Office & Stationery

Desk space planning, paper sizes (A4, Letter), and printer coverage areas are all rectangular area problems.

Common Rectangle Measurements

Object Length Width Area Perimeter Diagonal
📄 A4 Paper 29.7 cm 21 cm 623.7 cm² 101.4 cm 36.4 cm
🚪 Standard door 2 m 0.9 m 1.8 m² 5.8 m 2.19 m
🛏️ King bed 203 cm 193 cm 39179 cm² 792 cm 280 cm
⚽ Football pitch 100 m 64 m 6400 m² 328 m 118.5 m
🎾 Tennis court 23.77 m 10.97 m 260.8 m² 69.5 m 26.0 m
💳 Credit card 85.6 mm 54 mm 4622 mm² 279.2 mm 101.3 mm

Frequently Asked Questions

What is the formula for area of a rectangle?
A = l × w (length times width). For a rectangle 6 m × 4 m: A = 24 m². The result is always in square units (cm², m², etc.).
How do you find the diagonal of a rectangle?
Use Pythagoras' theorem: d = √(l² + w²). The diagonal is the hypotenuse of the right triangle formed by the length and width. For l=6, w=4: d = √52 ≈ 7.21.
What's the difference between area and perimeter of a rectangle?
Area = l × w — the space enclosed inside (measured in square units, e.g. m²). Perimeter = 2(l+w) — the total boundary length (measured in linear units, e.g. m). Think: area = carpet needed; perimeter = fence length.
How do you find length if you know area and width?
Rearrange A = l × w: l = A ÷ w. For A = 24 m² and w = 4 m: l = 24 ÷ 4 = 6 m. Similarly, w = A ÷ l.
Can a square be a rectangle?
Yes — a square is a special rectangle where l = w = s. Its area formula simplifies to A = s², and its diagonal is d = s√2. Every square is a rectangle, but not every rectangle is a square.
How does doubling both sides affect the area?
It quadruples the area. If both l and w double: A = (2l)(2w) = 4lw — exactly 4× the original. This is because area is proportional to both dimensions multiplied together.

Related Calculators

Area of a Circle Area of a Semicircle Area of a Square Area of a Rectangle Area of a Parallelogram Area of a Rhombus Area of a Trapezium Area of a Scalene Triangle Area of a Right Angle Triangle Area of an Equilateral Triangle Area of an Isosceles Triangle Area of a Regular Hexagon Area of Sector & Segment