What is area?
Area is the amount of flat surface a shape covers, measured in square units. Use it to find how much flooring, paint, turf or fabric a job needs, or to compare the size of two surfaces.
Area formulas for common shapes
| Shape | Formula |
|---|---|
| Rectangle | length × width |
| Square | side² |
| Triangle | ½ × base × height |
| Circle | π × radius² |
| Parallelogram | base × height |
| Trapezoid | ½ × (a + b) × height |
Worked examples
Flooring for a room
A room measures 5 m by 4 m, so the area is 5 × 4 = 20 square metres. Add about 10% extra for cuts and waste when you order materials.
A triangular garden bed
With a base of 6 m and a height of 4 m, the area is ½ × 6 × 4 = 12 square metres.
A circular table top
A table with radius 3 has area π × 3² = 9π, which is about 28.27 square units.
A trapezoid plot
Parallel sides of 5 and 9 with a height of 4 give ½ × (5 + 9) × 4 = 28 square units.
Units and conversion
Keep every measurement in the same unit before you multiply. Area units are squared, so converting them squares the length factor: 1 square metre equals 10,000 square centimetres, not 100. To find the volume of a solid built on these shapes, use the volume calculator.
Common area mistakes
The most common error is using a slanted side as the height of a triangle or parallelogram; the height is always perpendicular to the base. Another is entering the diameter where the circle formula needs the radius, which makes the answer four times too large. Finally, mixing units, such as metres and centimetres, gives a meaningless result. For circles, the circle calculator works from any one measurement.
Frequently asked questions
What is the formula for the area of a rectangle?
Multiply the length by the width. A room 5 metres long and 4 metres wide has an area of 5 × 4 = 20 square metres. The same rule works for any rectangle, as long as both sides use the same unit.
How do you find the area of a triangle?
Multiply the base by the perpendicular height, then halve the result. A triangle with base 6 and height 4 has area ½ × 6 × 4 = 12. The height must meet the base at a right angle, not run along a slanted side.
How do you calculate the area of a circle?
Square the radius and multiply by pi: A = πr². A circle with radius 3 has area π × 9, which is about 28.27. If you know the diameter, halve it first to get the radius.
Why is area measured in square units?
Area counts how many unit squares fit inside a shape, so the unit is squared: square metres, square centimetres or square feet. Multiplying two lengths in metres gives metres squared, which is why a length unit alone cannot describe an area.
How do you convert square metres to square centimetres?
Multiply by 10,000. One metre is 100 centimetres, and area squares that factor, so 1 square metre is 100 × 100 = 10,000 square centimetres. Converting length units and area units uses different factors, which is a common source of mistakes.
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Related topics on this page: area of a rectangle, area of a triangle, area of a circle, trapezoid area, square units, flooring and paint estimates