Area of a Sector Calculator
Calculate the area, arc length, and chord length of a circular sector from its radius and central angle. See also Arc Length Calculator and Area of Circle Calculator.
How to Calculate the Area of a Sector
A sector is a "pie slice" of a circle defined by two radii and the arc between them. To find the area, you need the radius and the central angle. If the angle is in degrees, use A = (θ/360) × πr². If in radians, use A = ½r²θ. The arc length is the curved edge of the sector, and the chord length is the straight line connecting the two endpoints of the arc.
Sector Area Formula
A = ½ × r² × θ (θ in radians)
A = (θ/360) × π × r² (θ in degrees)
Arc Length = r × θ (radians)
Chord Length = 2r × sin(θ/2)
Example
Find the area of a sector with radius 10 and angle 60°:
A = (60/360) × π × 10²
A = (1/6) × π × 100
A ≈ 52.3599 square units
Arc Length = 10 × (π/3) ≈ 10.4720
Chord Length = 2 × 10 × sin(30°) = 10
Sector Area Reference Table
| Radius | Angle (°) | Area | Arc Length |
|---|---|---|---|
| 5 | 30° | 6.5450 | 2.6180 |
| 5 | 60° | 13.0900 | 5.2360 |
| 5 | 90° | 19.6350 | 7.8540 |
| 10 | 30° | 26.1799 | 5.2360 |
| 10 | 60° | 52.3599 | 10.4720 |
| 10 | 90° | 78.5398 | 15.7080 |
| 10 | 120° | 104.7198 | 20.9440 |
| 10 | 180° | 157.0796 | 31.4159 |
| 10 | 270° | 235.6194 | 47.1239 |
| 10 | 360° | 314.1593 | 62.8319 |
| 15 | 45° | 88.3573 | 11.7810 |
| 20 | 60° | 209.4395 | 20.9440 |
Frequently Asked Questions
What is a sector?
A sector is a region of a circle enclosed by two radii and the arc between them — like a slice of pizza or pie. The central angle determines what fraction of the full circle the sector represents.
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc (pie slice shape). A segment is bounded by a chord and an arc. The segment area = sector area − triangle area formed by the two radii and the chord.
How do I convert between degrees and radians?
Multiply degrees by π/180 to get radians. Multiply radians by 180/π to get degrees. For example, 90° = π/2 radians, and π radians = 180°.
What is the area of a semicircle?
A semicircle is a sector with angle 180° (π radians). Its area is half the full circle: A = πr²/2.