Area measures the two-dimensional space enclosed by a flat shape. Whether you need to tile a floor, seed a lawn, or size a solar panel, area is the calculation you reach for. This guide walks through the five most common 2D shapes with step-by-step examples.
What Is Area?
Area is the amount of surface inside a 2D boundary, measured in square units — cm², m², ft², in², km², or acres. One square metre equals 10.764 square feet.
Circle Area: A = πr²
Where r = radius (distance from center to edge), π ≈ 3.14159.
The Circle Area Calculator uses this formula. If you know the diameter, halve it first: r = d/2.
Example: A circular garden with radius 4 m → A = π × 16 = 50.27 m². You need about 50 m² of sod.
Rectangle Area: A = l × w
Where l = length, w = width.
The Rectangle Area Calculator handles this instantly. Rectangles cover rooms, screens, fields, and walls.
Example: A room 5 m × 4 m → A = 20 m². For flooring, also see the Square Footage Calculator.
Triangle Area: A = ½bh
Where b = base length, h = perpendicular height from base to opposite vertex.
Use the Triangle Area Calculator. The height must be perpendicular to the base — slant sides do not count.
Example: A triangle with base 10 cm and height 6 cm → A = ½ × 10 × 6 = 30 cm².
Square Area: A = a²
Where a = side length. A square is a special rectangle where l = w.
The Square Area Calculator gives instant results. Squares appear in tiles, floor grids, and plot layouts.
Example: A tile 30 cm × 30 cm → A = 900 cm² = 0.09 m². You need about 112 tiles per 10 m².
Trapezoid Area: A = ½(a + b)h
Where a and b = the two parallel sides, h = perpendicular distance between them.
Use the Trapezoid Area Calculator. Trapezoids appear in roof profiles, bridge cross-sections, and land plots.
Example: Parallel sides 8 m and 5 m, height 4 m → A = ½(8 + 5) × 4 = 26 m².
Complete Formula Reference Table
| Shape | Formula | Variables |
|---|---|---|
| Circle | A = πr² | r = radius |
| Rectangle | A = l × w | l = length, w = width |
| Triangle | A = ½bh | b = base, h = height |
| Square | A = a² | a = side |
| Trapezoid | A = ½(a+b)h | a,b = parallel sides, h = height |
Step-by-Step Method for Any Shape
- Identify the shape — circle, rectangle, triangle, square, or trapezoid.
- Measure the required dimensions in the same unit (all cm, all m, etc.).
- Apply the formula — substitute your numbers.
- Calculate and label — include square units in the answer.
- Verify — use the Area Calculator or estimate mentally (e.g., a 3×4 rectangle ≈ 12).
Common Area Mistakes
- Using diameter instead of radius for circles (makes the answer 4× too large).
- Forgetting the ½ factor for triangles and trapezoids.
- Mixing units — convert all dimensions to the same unit before multiplying.
- Using slant height instead of perpendicular height for triangles.
- Forgetting square units — area is m², not m.
Area vs Surface Area vs Volume
| Concept | Dimensions | Units | Measures |
|---|---|---|---|
| Area | 2D | m², cm², ft² | Flat space |
| Surface Area | 3D outside | m², cm², ft² | Outside wrapping |
| Volume | 3D inside | m³, cm³, L | Enclosed space |
Related Calculators and Articles
Use the Area Calculator for quick calculations, or dive into specific shapes: Circle, Rectangle, Triangle, Square, Trapezoid, and Square Footage.
For 3D counterparts, see the Sphere Surface Area Calculator, Rectangular Prism Calculator, and Cylinder Volume Calculator. Also read our Area Formulas Cheat Sheet and Square Footage Measurement Guide.