A practical reference for calculating the area of any shape — from basic rectangles to irregular polygons. Formulas, worked examples, and real-world applications.
Area is the measure of the two-dimensional space inside a shape's boundaries. It's expressed in square units — square feet, square meters, acres, hectares — and it comes up constantly in everyday life. You need area to figure out how much flooring to buy, how much paint to order, whether a piece of furniture will fit in a room, or how much land you're actually purchasing.
Despite being one of the most practical concepts in math, many people only remember a couple of formulas from school. This guide covers every common shape you'll encounter, with clear formulas and real examples so you can calculate area confidently in any situation.
Rectangles and squares are the most common shapes you'll calculate area for. Floors, walls, screens, yards, and countless other everyday objects are rectangular.
Area = length × width
Your living room is 14 feet long and 12 feet wide.
Area = 14 × 12 = 168 square feet
If flooring costs $4.50 per square foot, you need 168 × $4.50 = $756 worth of flooring. Add 10% for waste: $831.60.
A square is a rectangle where all sides are equal, so the formula simplifies to:
Area = side × side = side²
A room that's 10 feet by 10 feet has an area of 100 square feet.
Circular areas come up when you're working with round tables, pools, gardens, pipes, and similar objects. The formula involves π (pi), which is approximately 3.14159.
Area = π × r²
Where r is the radius (half the diameter). If you only know the diameter, divide it by 2 to get the radius.
Your round table has a diameter of 48 inches.
Radius = 48 ÷ 2 = 24 inches
Area = π × 24² = π × 576 ≈ 1,810 square inches
To convert to square feet: 1,810 ÷ 144 = 12.57 square feet.
Triangles appear in roofing, landscaping, and design. The basic formula works for any triangle as long as you know the base and height.
Area = ½ × base × height
Your garden bed has a base of 8 feet and a height of 5 feet.
Area = ½ × 8 × 5 = 20 square feet
If mulch covers 1 cubic foot per 2 square feet at 2 inches deep, you need 10 cubic feet of mulch.
For a right triangle, the two legs (sides that form the 90° angle) serve as the base and height. Area = ½ × leg₁ × leg₂. This is especially useful in construction and woodworking.
If you know all three sides of a triangle but not the height, use Heron's formula:
s = (a + b + c) ÷ 2 Area = √(s(s − a)(s − b)(s − c))
Where s is the semi-perimeter, and a, b, c are the three side lengths.
s = (7 + 8 + 9) ÷ 2 = 12
Area = √(12 × 5 × 4 × 3) = √720 ≈ 26.83 square units
A trapezoid has two parallel sides (bases) of different lengths, connected by non-parallel sides. Trapezoidal shapes are common in architecture, road design, and landscaping.
Area = ½ × (base₁ + base₂) × height
Your driveway is 20 feet wide at the street, 14 feet wide at the garage, and 40 feet long.
Area = ½ × (20 + 14) × 40 = ½ × 34 × 40 = 680 square feet
An ellipse is an elongated circle. You'll encounter them with oval tables, running tracks, and garden features.
Area = π × a × b
Where a and b are the semi-major and semi-minor axes (half the longest and shortest diameters).
Pool dimensions: 30 feet long × 16 feet wide.
a = 15, b = 8
Area = π × 15 × 8 ≈ 377 square feet
Real-world spaces rarely fit perfectly into one geometric shape. The solution is to break the area into simpler shapes, calculate each one, and add them together.
An L-shaped room can be divided into two rectangles. For example, if the room consists of a 12×10 rectangle and a 6×8 rectangle:
Area = (12 × 10) + (6 × 8) = 120 + 48 = 168 square feet
A semicircular patio attached to a rectangular deck: calculate the rectangle's area and add half the area of a circle. A hexagonal gazebo: divide it into 6 equilateral triangles and sum them. The decomposition approach works for virtually any shape you'll encounter.
| From | To | Multiply By |
|---|---|---|
| Square feet | Square meters | 0.0929 |
| Square meters | Square feet | 10.764 |
| Square feet | Square yards | 0.1111 |
| Acres | Square feet | 43,560 |
| Hectares | Acres | 2.471 |
| Square inches | Square feet | 0.00694 |
To calculate how much paint you need: measure the wall area (height × perimeter), subtract windows and doors, then divide by the coverage rate (typically 350–400 sq ft per gallon). A 10×12 room with 8-foot ceilings has about 352 square feet of wall area — roughly one gallon for two coats.
For mulch, gravel, or soil, calculate the surface area first, then multiply by the desired depth to get cubic volume. A 200 sq ft garden bed at 3 inches deep needs: 200 × (3÷12) = 50 cubic feet of material.
Property sizes are typically listed in square feet (US) or square meters (most other countries). Understanding area helps you compare properties, negotiate prices per square foot, and plan renovations accurately.
While knowing the formulas is essential, an online area calculator saves time and reduces errors — especially for complex shapes. Simply enter your dimensions, and the calculator handles the math instantly, often providing results in multiple units. This is particularly useful when you're comparing materials priced in different unit systems.