Circle Sector Square Footage Calculator
Enter your measurements below to get the area of a circle sector in square feet, square metres, square yards and acres. The live preview draws the circle sector to scale as you type, labelled on a measured grid, and you can drag its handles to change the measurements.
Area = π × Radius² × (Angle ÷ 360)
Live scale preview
The shape is drawn to scale and relabelled as you type.
An example to start from. Drag a handle or type a measurement and it becomes yours.
Worked example
A circle sector with radius 10 ft, angle 90° works out at 78.54 square feet.
| Unit | Area |
|---|---|
| sq ft | 78.54 |
| m² | 7.3 |
| sq yd | 8.73 |
| sq in | 11,310 |
| acres | 0.001803 |
When to use the sector calculator
A sector is a slice of a circle — the pie-slice shape between two radii and the arc joining them. On site that means rounded patio corners, fan-shaped decks, curved driveway aprons, pie-slice garden beds, the half-round end of a pool, and the swing area a door sweeps on a floor plan.
The formula takes the fraction of the whole circle that your angle covers: π × radius² × (angle ÷ 360). A quarter-circle patio corner with a 10 ft radius is 3.14159 × 100 × 0.25 = 78.54 square feet.
Sectors and semicircles are also covered in the guide to calculating the square footage of a circle.
Working out the angle without a protractor
Most sectors on a building site are one of a handful of obvious cases. A rounded corner cut from a rectangle is 90 degrees. A half-round bay or pool end is 180 degrees. A three-quarter fan around an inside corner is 270. If your shape is one of these, you can enter the angle with confidence and skip any measuring.
For anything in between, measure the radius and then the straight-line distance between the two ends of the curve. If that chord is about 1.41 times the radius the angle is 90 degrees; if it equals the radius it is 60. When you genuinely cannot tell, round the angle up rather than down — over-ordering by a few square feet costs far less than a second delivery.
Combining a sector with other shapes
Curved shapes rarely stand alone. A patio with two rounded corners is a rectangle plus two quarter-circle sectors; a stadium-shaped pool is a rectangle plus a half-circle at each end. Add each piece as its own row in the multi-room calculator to get one total, and allow 15% to 20% waste on any material that has to be cut to follow the arc.
Frequently asked questions
How do I calculate the square footage of a circle sector?
Work out the area of the whole circle, then take the fraction of it your angle covers. The formula is π × radius² × (angle ÷ 360). A quarter-circle patio with a 10 ft radius is 3.14159 × 100 × (90 ÷ 360) = 78.54 square feet.
How do I measure the angle of a sector on site?
You usually do not need a protractor. Measure the radius, then measure the straight-line distance between the two ends of the curve — the chord. For the common cases the angle is obvious anyway: a quarter-circle corner is 90 degrees, a half-round bay is 180 degrees, and a rounded corner cut off a rectangle is 90 degrees. If in doubt, treat it as a quarter-circle and add waste.
Where do sector areas come up in a project?
Rounded patio corners, fan-shaped decks, curved driveway aprons, the swing area of a door on a floor plan, and pie-slice garden beds. They also cover half-round pool ends: a kidney or oval pool cover is often best estimated as a rectangle with a sector at each end.
Other shapes
A space that is not a circle sector can nearly always be split into two or three of these and added together.
- Circle calculator
- L-Shaped Room calculator
- Parallelogram calculator
- Rectangle calculator
- Square calculator
- Trapezoid calculator
- Triangle calculator
- Triangle (Three Sides) calculator
To add several spaces into one figure, use the multi-room square footage calculator. To turn this area into an order quantity, see the material calculators.
New to the math? The square footage formula for every shape explains the calculation behind each of these tools.