How to find the area of a circle
Measure straight across the circle through its middle — the diameter — then multiply it by itself and by π ÷ 4, which is 0.7854. A circle 10 feet across is 10 × 10 × 0.7854 = 78.54 square feet. If you have the radius instead, the distance from the middle to the edge, the formula you learned in school gives the same answer: π × 5 × 5 = 78.54. The radius is half the diameter, so double it and type that into the box.
This page asks for the diameter because it is the one you can measure. The middle of a patio or a rug is not marked, and a tape run from a guessed center to the edge is a guess. Across is easy to check: measure the widest distance two or three times at different angles, and if the readings differ, the shape is not quite a circle — use the average, or the largest if you are buying material to cover it.
The distance round the edge, the circumference, is π times the diameter: 31.42 feet for a 10 foot circle. That is the figure for edging, a flexible border or a strip of trim.
Circle areas by diameter
| Across | Area | Square yards | Round the edge |
|---|---|---|---|
| 4 ft | 12.57 ft² | 1.40 | 12.57 ft |
| 6 ft | 28.27 ft² | 3.14 | 18.85 ft |
| 8 ft | 50.27 ft² | 5.59 | 25.13 ft |
| 10 ft | 78.54 ft² | 8.73 | 31.42 ft |
| 12 ft | 113.10 ft² | 12.57 | 37.70 ft |
| 16 ft | 201.06 ft² | 22.34 | 50.27 ft |
| 20 ft | 314.16 ft² | 34.91 | 62.83 ft |
Doubling the diameter makes four times the area, not twice: a 20 foot circle is 314 square feet, four 10 foot circles' worth. Guessing a size by eye goes wrong fastest on circles for that reason.
Rings and half circles
A path round a round bed or a pool is a ring: the big circle minus the small one. Choose Ring and type both diameters across the outside and the inside. A 3 foot path round a 10 foot bed is 16 feet across outside and 10 inside: 0.7854 × (16 × 16 − 10 × 10) = 122.52 square feet. Measuring the path's width and multiplying by the circumference gets close but not exact, because the outer edge of the path is longer than the inner one.
A half circle or a quarter is a pie slice: type the diameter of the full circle and the angle, 180 for a half and 90 for a quarter. A half circle 10 feet across is 39.27 square feet. Round the edge it is 25.71 feet, the curve plus the straight side.
Feet, inches and meters
Type the diameter the way the tape reads it, in one box: 12' 6"
is 12.5 feet, and a circle that size is 122.72 square feet. Squaring makes a
misread inch count twice, so check the line under the box that says what it
read. The area is also shown in square yards, square meters and acres; a 10
foot circle is 7.30 square meters.
Common questions
What is the area of a circle with a diameter of 10 feet?
78.54 square feet: 10 × 10 × π ÷ 4. Its radius is 5 feet, and π × 5 × 5 gives the same 78.54.
How do I find the area from the circumference?
Divide the circumference by π to get the diameter, then use that. A circle 31.42 feet round is 10 feet across, and 78.54 square feet.
Why not use 3.14 for π?
3.14 is close enough to talk about and 0.05% short. This page uses π to the precision of the computer, so the number above does not depend on how many digits anyone remembered.
Can I add a circle to a room?
Yes. Add an area for each piece — a rectangle for the room, a half circle for a bay — and the total adds them. The square footage calculator offers every shape in one picker.