Area Calculator
Pick a shape, enter its measurements, and get the area and perimeter, plus the same area in other common units.
Area formulas for common shapes
Area is the amount of surface inside a shape. These are the formulas the calculator uses.
| Shape | Area formula |
|---|---|
| Rectangle | length × width |
| Square | side × side |
| Triangle (base and height) | ½ × base × height |
| Triangle (three sides) | Heron’s formula: √(s(s − a)(s − b)(s − c)), where s is half the perimeter |
| Circle | π × radius² |
| Ellipse | π × a × b, where a and b are the two radii |
| Trapezoid | ½ × (base 1 + base 2) × height |
| Parallelogram | base × height |
| Circle sector | (angle ÷ 360) × π × radius² |
How to use the area calculator
- Choose the shape that matches what you are measuring.
- Choose the unit you measured in. All measurements should be in the same unit.
- Enter the measurements. The area appears as you type, along with the perimeter where it can be worked out.
- Read the same area in other units, from square inches to acres and hectares.
Worked examples
ExampleRectangle. A patio 20 ft by 12 ft has an area of 20 × 12 = 240 sq ft.
ExampleCircle. A round patio with a 10 ft radius has an area of π × 10² = 314.16 sq ft. If you only know the diameter (20 ft), choose “Circle (from diameter)”.
ExampleTriangle. A garden bed with a 6 ft base and a 4 ft height has an area of ½ × 6 × 4 = 12 sq ft.
ExampleTrapezoid. A lawn with parallel sides of 8 ft and 12 ft, 5 ft apart, has an area of ½ × (8 + 12) × 5 = 50 sq ft.
Area of a circle by diameter
Round tables, patios, pools and garden beds are usually measured across the middle. This table gives the area for common diameters.
| Diameter (ft) | Radius (ft) | Area (sq ft) |
|---|---|---|
| 4 | 2 | 12.57 |
| 6 | 3 | 28.27 |
| 8 | 4 | 50.27 |
| 10 | 5 | 78.54 |
| 12 | 6 | 113.1 |
| 15 | 7.5 | 176.71 |
| 20 | 10 | 314.16 |
| 24 | 12 | 452.39 |
Area versus perimeter
Area is measured in square units and tells you how much surface there is, which is what you need for flooring, paint, sod or seed. Perimeter is measured in plain units and tells you the distance around the edge, which is what you need for fencing, edging or trim. Two shapes can have the same perimeter and very different areas, so always work out the one your project needs.
Finding the area of an irregular shape
Split the shape into simple pieces, find the area of each one, and add them up. If a piece is cut out of the shape, work it out separately and subtract it. To add up several rectangles at once, use our square footage calculator.
Area unit conversions
| Unit | Equals |
|---|---|
| 1 square foot | 144 square inches |
| 1 square yard | 9 square feet |
| 1 square meter | 10.764 square feet |
| 1 acre | 43,560 square feet, or 4,840 square yards |
| 1 hectare | 10,000 square meters, or about 2.471 acres |
| 1 square mile | 640 acres |
Results are estimates based on the numbers you enter. Confirm quantities with your supplier, installer or contractor before ordering.
Frequently asked questions
How do I find the area of a circle if I only know the diameter?
Divide the diameter by 2 to get the radius, then use π × radius². A circle 10 ft across has a 5 ft radius and an area of about 78.54 sq ft.
What units is the answer in?
Area is shown in square units of whatever unit you pick. The extra figures show the same area in square inches, square feet, square yards, square meters, acres and hectares.
What is the difference between area and perimeter?
Area is the amount of surface inside a shape, measured in square units. Perimeter is the distance around the outside. You need area for flooring, paint or sod, and perimeter for fencing or trim.
Why does the triangle (three sides) option sometimes show an error?
Three lengths only make a triangle if the two shorter sides add up to more than the longest side. If they do not, the sides cannot form a closed triangle.
How do I find the area of an irregular shape?
Split it into rectangles, triangles and circles, find the area of each piece, and add them. Subtract any piece that is cut out.
How do I convert square feet to acres?
Divide the square feet by 43,560. For example, 10,000 sq ft is about 0.23 acres.
How accurate are the results?
The formulas are exact, so accuracy depends on your measurements. The one exception is the perimeter of an ellipse, which has no simple exact formula; the calculator uses Ramanujan’s approximation.