Area measures the size of a two‑dimensional surface. It’s used everywhere—from paint estimates to land size. This guide covers units, formulas, conversions, and applications.
What is Area?
Area is the extent of a surface within a boundary, expressed in square units (how many unit squares cover it).
Key Concept:
Think of area as the “space” inside a shape. A sheet of paper ≈ 0.06 m² (~93 in²).
Common Units of Area
Metric System
- Square millimeter (mm²) — 1/1,000,000 m²
- Square centimeter (cm²) — 1/10,000 m²
- Square meter (m²) — Base unit
- Are (a) — 100 m²
- Hectare (ha) — 10,000 m²
- Square kilometer (km²) — 1,000,000 m²
Imperial/US Customary
- Square inch (in²) — 1/144 ft²
- Square foot (ft²) — 144 in²
- Square yard (yd²) — 9 ft²
- Square mile (mi²) — 27,878,400 ft²
- Acre — 43,560 ft²
Calculating Area of Common Shapes
Rectangle
Area = length × width
Example: 4 m × 5 m room → 20 m²
Triangle
Area = ½ × base × height
Example: base 6 m, height 4 m → 12 m²
Circle
Area = π × radius²
Example: radius 3 m → ~28.27 m²
Converting Between Area Units
| From | To | Multiply By |
|---|---|---|
| Square meters (m²) | Square feet (ft²) | 10.764 |
| Square feet (ft²) | Square meters (m²) | 0.0929 |
| Acres | Square meters (m²) | 4,046.86 |
| Hectares (ha) | Acres | 2.471 |
Practical Applications of Area
Construction
- Flooring/roofing materials
- Paint/wallpaper quantities
- Room layouts and furniture
Agriculture
- Field size measurement
- Seed/fertilizer estimates
- Irrigation planning
Real Estate
- Property valuation
- Zoning compliance
- Space planning
Manufacturing
- Material usage
- Packaging design
- Facility layout
Did You Know?
Russia ≈ 17.1 million km² (largest); Vatican City ≈ 0.49 km² (smallest).
Common Area Conversions
Metric to Imperial
- 1 m² = 10.764 ft²
- 1 hectare = 2.471 acres
- 1 km² = 0.386 mi²
- 1 cm² = 0.155 in²
Imperial to Metric
- 1 ft² = 0.093 m²
- 1 acre = 0.405 hectares
- 1 mi² = 2.59 km²
- 1 in² = 6.452 cm²
Practical Tip:
Break irregular shapes into rectangles/triangles, compute each, then sum for total area.