Circle Sqft Calculator
Measure straight across the widest point for the diameter — it is far easier to get right than the radius.
To find the square footage of a circle, multiply π by the diameter squared, then divide by 4. A circle 10 ft across is (3.14159 × 10 × 10) ÷ 4 = 78.54 square feet. If you know the radius instead, the formula is π × radius².
Formula: π × d² ÷ 4
Formula: π × r²
Formula: π × a × b ÷ 4
The circle area formula
Both versions give the same answer — use whichever measurement you actually have:
- From diameter: Area = π × d² ÷ 4
- From radius: Area = π × r²
Measure the diameter if you can. Finding the exact center of a circle in order to measure a radius is surprisingly error-prone, and any mistake gets squared. Running a tape across the widest point is far more reliable.
A worked example
A round patio measures 14 feet across.
- Square the diameter: 14 × 14 = 196
- Multiply by π: 196 × 3.14159 = 615.75
- Divide by 4: 615.75 ÷ 4 = 153.94 square feet
At $12 per square foot for pavers, that patio costs 153.94 × $12 = $1,847 in materials, before waste.
Half circles, quarter circles and rings
Fractions of a circle are straightforward — calculate the full circle, then take the fraction:
- Semicircle: full area ÷ 2
- Quarter circle: full area ÷ 4
- Ring or border: outer circle area − inner circle area
For a circular path 3 ft wide around a 20 ft pool: the outer circle is 26 ft across (530.93 sq ft), the inner is 20 ft (314.16 sq ft), so the path is 530.93 − 314.16 = 216.77 sq ft.
Circle square footage by diameter
| Diameter | Radius | Square feet |
|---|---|---|
| 4 ft | 2 ft | 12.57 sq ft |
| 6 ft | 3 ft | 28.27 sq ft |
| 8 ft | 4 ft | 50.27 sq ft |
| 10 ft | 5 ft | 78.54 sq ft |
| 12 ft | 6 ft | 113.10 sq ft |
| 15 ft | 7.5 ft | 176.71 sq ft |
| 18 ft | 9 ft | 254.47 sq ft |
| 20 ft | 10 ft | 314.16 sq ft |
| 24 ft | 12 ft | 452.39 sq ft |
Frequently asked questions
How do you calculate the sqft of a circle?
Multiply π (3.14159) by the diameter squared and divide by 4. For a circle 10 feet across: 3.14159 × 100 ÷ 4 = 78.54 square feet.
What is the square footage of a 12 foot circle?
A circle with a 12 foot diameter is 113.10 square feet. The calculation is 3.14159 × 12² ÷ 4 = 113.10.
Should I measure diameter or radius?
Measure the diameter. Finding the exact center of a circle is difficult and any error is squared in the formula, whereas running a tape across the widest point is easy to do accurately.
How do I calculate the area of a half circle?
Work out the full circle area, then divide by two. A semicircle with a 10 foot diameter is 78.54 ÷ 2 = 39.27 square feet.
How do I find the square footage of a round pool?
Measure the diameter of the water surface and apply the circle formula. For a 20 foot round pool: 3.14159 × 400 ÷ 4 = 314.16 square feet — the figure you need for a pool cover or solar blanket.