How to Calculate Area & Perimeter
Every formula you need for the four most common shapes — with worked examples in both metric and imperial.
Key formulas: Rectangle area = length × width. Circle area = πr². Triangle area = ½ × base × height. Perimeter = sum of all sides (rectangle: 2l + 2w; circle circumference: 2πr). Units: area is always in square units (m², ft², cm²); perimeter is in linear units (m, ft, cm).
Step-by-Step
Measure the lengths you need for that shape. A rectangle needs length and width (e.g. 8 m × 3 m); a circle needs the radius (e.g. 7 cm); a triangle needs base and perpendicular height.
Use the formula for your shape. Rectangle area = length × width = 8 × 3 = 24 m². Circle area = πr². Triangle area = ½ × base × height.
Add all the sides, or use the circumference formula for a circle. Rectangle perimeter = 2l + 2w = 2(8) + 2(3) = 22 m. Circle circumference = 2πr.
Area is always in square units (m², ft², cm²); perimeter is in linear units (m, ft, cm). Mixing the two is the most common mistake.
Formula Reference Table
| Shape | Area | Perimeter | Variables |
|---|---|---|---|
| Square | s² | 4s | s = side length |
| Rectangle | l × w | 2l + 2w | l = length, w = width |
| Triangle | ½ × b × h | a + b + c | b = base, h = perpendicular height, a/b/c = sides |
| Circle | πr² | 2πr (circumference) | r = radius, π ≈ 3.14159 |
| Trapezoid | ½(a+b)h | a + b + c + d | a, b = parallel sides, h = height, c, d = other sides |
| Parallelogram | b × h | 2(a + b) | b = base, h = perpendicular height, a = adjacent side |
Worked Examples
Metric vs Imperial Area Units
- Metric (most of the world): mm², cm², m², km², hectares (ha). 1 ha = 10,000 m² (a football pitch ≈ 0.7 ha).
- US/Imperial: sq inches (in²), sq feet (ft²), sq yards (yd²), acres, sq miles. 1 acre = 43,560 ft².
- Key conversions: 1 m² = 10.764 ft². 1 acre = 0.4047 hectares. 1 hectare = 2.471 acres.
- Real estate: US lists in sq ft; UK, Europe, Australia use m²; India uses sq ft (common) or gaj/bigha (traditional units).