Circle Sector Area Calculator
Calculate the area of a circle sector from the radius and central angle in degrees. Formula: Area = (theta/360) x pi x r^2. Fast and free.
How to use this tool
- Enter radius (r) and central angle in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your sector area and the full breakdown beneath it.
Formula
Area = (theta / 360) x pi x r^2; Arc Length = (theta / 360) x 2 x pi x r
How it works
A sector is a pie-slice of a circle. Divide the central angle by 360 to get the fraction of the full circle, then multiply by the full circle area (pi x r^2) for the sector area.
Worked example
Quarter-circle sector (90 degrees), radius 6 m
- Fraction = 90 / 360 = 0.25
- Sector Area = 0.25 x pi x 6^2 = 0.25 x pi x 36 = 9 x pi = 28.2743 m^2
28.2743 m^2
Common mistakes to avoid
- Entering the angle in radians when the formula expects degrees; confirm which unit the calculator uses before entering theta.
- Confusing the sector area with the triangle area of the same slice; the sector includes the curved arc, the triangle does not.
- Using the chord length (straight line between arc endpoints) as the arc length; arc length follows the curve and is always longer than the chord.
Key terms
- What is a circle sector?
- The region bounded by two radii and the arc between them -- like a pizza slice.
- What is the central angle?
- The angle at the center of the circle between the two radii that form the sector.
Frequently asked questions
- What is the difference between a sector and a segment of a circle?
- A sector is the pie-slice shape bounded by two radii and the arc. A segment is the region between a chord and the arc, excluding the central triangle.
- How do I convert my angle from radians to degrees?
- Multiply radians by (180/pi). For example, pi/3 radians = 60 degrees.
- What happens if theta = 360 degrees?
- The sector becomes the full circle, and Area = (360/360) x pi x r^2 = pi x r^2, which matches the circle area formula.