How to Calculate Area and Perimeter: Complete Guide with Formulas
Last updated: December 2024 • 10 min read
Whether you're laying new flooring, painting a room, building a fence, or solving geometry problems, knowing how to calculate area and perimeter is essential. This comprehensive guide covers formulas for all common shapes, with practical examples you can apply immediately.
Area vs. Perimeter: What's the Difference?
Area
The space inside a shape. Measured in square units (m², ft², cm²).
Use for: Flooring, painting, grass seed, fabric
Perimeter
The distance around a shape. Measured in linear units (m, ft, cm).
Use for: Fencing, trim, borders, framing
Rectangle
The most common shape you'll encounter in everyday calculations.
Area = length × width
Perimeter = 2 × (length + width)
Example: A Room 5m × 4m
Area = 5 × 4 = 20 m² (for flooring/carpet)
Perimeter = 2 × (5 + 4) = 2 × 9 = 18 m (for baseboards)
Square
A special rectangle where all sides are equal.
Area = side²
Perimeter = 4 × side
Example: A 3m × 3m Patio
Area = 3² = 9 m²
Perimeter = 4 × 3 = 12 m
Triangle
Area = ½ × base × height
Perimeter = side₁ + side₂ + side₃
Example: Triangle with base 6m, height 4m
Area = ½ × 6 × 4 = 12 m²
Note: The height must be perpendicular to the base.
Circle
Area = π × radius² (π ≈ 3.14159)
Circumference = 2 × π × radius or π × diameter
Example: Circle with radius 3m
Area = π × 3² = 3.14159 × 9 = 28.27 m²
Circumference = 2 × π × 3 = 18.85 m
Trapezoid
Common in architectural features and irregular plots.
Area = ½ × (base₁ + base₂) × height
Perimeter = sum of all four sides
Example: Trapezoid with parallel sides 8m and 5m, height 4m
Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 m²
Parallelogram
Area = base × height
Perimeter = 2 × (side₁ + side₂)
Quick Reference Table
| Shape | Area Formula | Perimeter Formula |
|---|---|---|
| Rectangle | l × w | 2(l + w) |
| Square | s² | 4s |
| Triangle | ½ × b × h | a + b + c |
| Circle | πr² | 2πr |
| Trapezoid | ½(a+b)h | sum of sides |
| Parallelogram | b × h | 2(a + b) |
Practical Applications
1. Buying Flooring
Room: 4.5m × 3.2m
Area = 4.5 × 3.2 = 14.4 m²
Tip: Add 10% for waste → 14.4 × 1.1 = 15.84 m² needed
2. Building a Fence
Yard: 20m × 15m rectangle
Perimeter = 2 × (20 + 15) = 70m of fencing needed
If fence posts are every 2m: 70 ÷ 2 = 35 posts
3. Painting a Wall
Wall: 5m wide × 2.5m tall with a 2m × 1m window
Wall area = 5 × 2.5 = 12.5 m²
Window area = 2 × 1 = 2 m²
Paintable area = 12.5 - 2 = 10.5 m²
Irregular Shapes
For complex shapes, divide them into simpler shapes, calculate each part, and add them together.
L-shaped room: Split into two rectangles
Total Area = Rectangle₁ Area + Rectangle₂ Area
Calculate Area and More
Use our calculator for quick area and perimeter calculations.
Try Calculator →Frequently Asked Questions
How do I convert between square meters and square feet?
1 m² = 10.764 ft². Multiply m² by 10.764 to get ft², or divide ft² by 10.764 to get m².
Why add extra when buying materials?
Adding 10-15% accounts for waste from cutting, mistakes, and future repairs. It's better to have a bit extra than to run short.
How do I measure an irregular room?
Break it into rectangles and triangles. Measure each section separately, calculate their areas, and add them together.