Area comes up more often in real life than most people expect. Painting a wall, laying turf, tiling a bathroom, buying carpet, calculating land size — all of these require area calculations. The maths isn't complicated, but there are enough different shapes to keep things interesting. Here's every formula you need, explained simply and with examples you'll actually encounter.
What Is Area?
Area is the amount of two-dimensional space inside a shape's boundary. It's measured in square units — square centimetres (cm²), square metres (m²), square feet (ft²), or square kilometres (km²). A 4m × 3m room has an area of 12m² — you'd need 12 one-metre square tiles to cover the floor.
Our square footage calculator handles area calculations for rooms and properties instantly. For tiling specifically, our tile calculator works out how many tiles you need once you know the area.
Square and Rectangle
Area = Length × Width
A square is just a rectangle where length equals width. A 5m × 8m room has an area of 40m². A 4m × 4m square room has an area of 16m². Straightforward.
Real-world use: calculating paint coverage, flooring, carpeting. Always add 10-15% waste for cutting and fitting.
Triangle
Area = ½ × Base × Height
The height must be perpendicular (at 90°) to the base — it's not the slanted side. A triangle with a 6m base and 4m height has an area of ½ × 6 × 4 = 12m².
For a triangle where you know all three sides but not the height, Heron's formula is your friend: A = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2. It's fiddly but works for any triangle.
Circle
Area = π × r²
Where π (pi) ≈ 3.14159 and r is the radius (half the diameter). A circular lawn with a 3m radius has an area of 3.14159 × 9 ≈ 28.3m².
If you know the diameter rather than the radius: r = diameter ÷ 2. So a 6m diameter circle has a 3m radius and the same 28.3m² area.
Trapezium (Trapezoid)
Area = ½ × (a + b) × h
Where a and b are the two parallel sides and h is the perpendicular height between them. Common in roof and land calculations where one boundary is longer than the other.
A trapezium with parallel sides of 8m and 5m and a height of 4m: ½ × (8+5) × 4 = ½ × 13 × 4 = 26m²
Parallelogram
Area = Base × Height
The height is perpendicular to the base (not the slanted side). A parallelogram with a 7m base and 3m height has an area of 21m². Note: this is the same formula as a rectangle, which makes sense because a parallelogram is essentially a rectangle that's been leaned to one side.
Irregular Shapes
Real-world spaces are rarely perfect rectangles. Common approaches:
- Break it down: divide the irregular shape into simpler shapes (rectangles, triangles), calculate each area, and add them together.
- The grid method: overlay a grid of known square size and count full squares plus estimate partial ones.
- The compensation method: for land or gardens, measure the overall bounding rectangle and subtract the areas of the corners that fall outside your actual space.
Converting Between Area Units
- 1 m² = 10,000 cm²
- 1 m² = 10.764 ft²
- 1 km² = 1,000,000 m² = 100 hectares
- 1 acre = 4,047 m²
Area conversions catch people out because the conversion factors are squared. 1 metre = 100 centimetres, but 1 square metre ≠ 100 square centimetres — it's 10,000 (100 × 100). Always square your unit conversion factor.
With these formulas in your toolkit, any area calculation becomes manageable — from the humble bathroom tile job to working out whether that allotment plot is the right size.
Further reading: Khan Academy has an excellent series on area calculations for all shapes. Practice area calculations at Khan Academy.