What is a sector?
A sector is the "pie slice" region of a circle bounded by two radii and the arc between them. Every sector is defined by two numbers: the radius of the circle and the central angle that subtends the arc.
Sector area: A = (θ / 360) × π × r² (when θ is in degrees)
If you prefer radians, use A = ½ × r² × θ.
How to use
- Enter the radius of the circle (any unit — the area comes back in that unit squared).
- Enter the angle in degrees. A full circle is 360°, a half-circle is 180°, a quarter is 90°.
- The sector area is calculated instantly.
For a circle of radius 10 with a 90° sector: A = (90/360) × π × 100 = ¼ × π × 100 ≈ 78.54 square units.
Special cases
- Full circle (θ = 360°): A = π × r² — the standard area of a circle.
- Half circle (θ = 180°): A = ½ × π × r².
- Quarter circle (θ = 90°): A = ¼ × π × r².
Why sector area matters
Sectors show up in pie charts, gear teeth, pizza slices, irrigation patterns, lighthouse beams, and any time you need to measure part of a circular region. Knowing the area lets you compute paint, fabric, land coverage, or proportional values.
FAQ
How is sector area different from segment area?
A sector is bounded by two radii and an arc (a pie slice). A segment is bounded by a chord and an arc (the part you'd cut off with a straight line). Segment area = sector area − triangle area.
What if my angle is in radians?
Multiply the radian value by 180/π to convert to degrees first, or use the formula A = ½ × r² × θ directly with θ in radians.
What about a sector of an ellipse?
This calculator only handles circular sectors. Elliptical sectors need a different formula because the radius varies with angle.