Pick a shape, enter the dimensions, get the area.
Area formulas
Rectangle A = length × width
Circle A = π × r² (circumference = 2πr)
Triangle A = ½ × base × height
Trapezoid A = ½ × (a + b) × h
Example: a 5 m × 4 m living room = 20 m². Flooring sold per m² at ¥150 would cost 20 × 150 = ¥3,000.
What is area and why calculate it?
Area measures the amount of space inside a two-dimensional shape. It is essential for home renovation, construction, real estate, gardening and craft projects. Knowing the area helps you buy the right amount of materials — flooring, paint, tiles, soil or fabric — and avoid waste or shortfalls.
How to calculate area for each shape
- Rectangle or square: Multiply length by width. A 6 m × 4 m room = 24 m². A square is just a rectangle with equal sides.
- Circle: A = π × r², where r is the radius (half the diameter). A 5 m radius circular patio = π × 25 ≈ 78.5 m².
- Triangle: A = ½ × base × height. A triangle with base 8 m and height 5 m = ½ × 8 × 5 = 20 m².
- Trapezoid: A = ½ × (a + b) × h, where a and b are the two parallel sides and h is the height between them.
- Irregular shapes: Divide the shape into rectangles and triangles, calculate each area, then add them together.
Common area units and conversions
| Unit | Equivalent | Typical use |
|---|
| 1 m² | 10,000 cm² | Rooms, flooring |
| 1 km² | 1,000,000 m² | Land, cities |
| 1 亩 (mu) | ≈ 666.67 m² | Farmland in China |
| 1 hectare | 10,000 m² = 15 亩 | Large land parcels |
| 1 acre | ≈ 4,046.86 m² | Land (US/UK) |
| 1 ft² | ≈ 0.0929 m² | Flooring (US/UK) |
Practical examples
- Flooring: A 5 m × 4 m room = 20 m². Add 10% waste = 22 m² of flooring needed.
- Painting: A wall 4 m wide × 2.6 m high = 10.4 m². One litre of paint covers ~10 m², so buy 1.5 litres for two coats.
- Garden soil: A 3 m × 2 m bed = 6 m². At 10 cm depth, you need 6 × 0.1 = 0.6 m³ of soil.
- Property size: A 120 m² apartment in China is roughly 1,292 ft². Farmland is measured in 亩 (1 亩 ≈ 666.67 m²).
Tips for accurate area calculation
- Measure twice. A small error in length becomes a bigger error in area (squared effect).
- Account for waste. Add 5–15% extra for cuts, breakage and mistakes when buying materials.
- Split complex shapes. For L-shaped or irregular rooms, divide into rectangles and sum the areas.
- Use consistent units. Convert all measurements to meters before calculating to get m² directly.
FAQ
How do I calculate the area of a rectangle?
Multiply the length by the width. For example, a 5 m × 4 m room has an area of 5 × 4 = 20 m².
What is the formula for the area of a circle?
A = π × r². For a circle with radius 5 m, area = π × 25 ≈ 78.5 m².
How many square meters is one mu?
1 亩 ≈ 666.67 m². 1 hectare = 15 亩.
How much extra flooring should I buy?
Add 5–15% extra for cuts, breakage and mistakes. For a 20 m² room, buy 21–23 m².
How do I calculate an irregular shape's area?
Divide it into simpler shapes (rectangles, triangles), calculate each area, then add them together.