Sector Area Calculator: Sector and Segment of a Circle
Enter the radius and the angle of the sector. You get the sector area, the segment area (between the chord and the arc), the arc length and more.
- Nothing you type is stored
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Sector area
153.938cm²
- Minor segment area
- 55.938 cm²
- Arc length
- 21.9911 cm
- Sector perimeter
- 49.9911 cm
- Major sector area
- 461.8141 cm²
Show working
- A = (θ / 360°) × πr² = (90 / 360) × π × 14² = 153.938 cm²
- l = (θ / 360°) × 2πr = 21.9911 cm
- ΔOAB = ½ r² sin θ = 98 cm²
- Segment = sector − ΔOAB = 153.938 − 98 = 55.938 cm²
How to use
- Enter the radius.
- Enter the angle and choose degrees or radians.
- Read the sector and segment areas with the steps.
Good to know
Sector area = (θ/360°) × πr², from NCERT Class 10 "Areas Related to Circles". The major sector is the rest of the circle, πr² minus the minor sector.
The minor segment is the area between the chord and the arc: sector area minus the triangle OAB, where the triangle's area is ½r² sin θ. For r = 14 cm and θ = 90° with π = 22/7, the sector is 154 cm² and the segment 56 cm².
Typical uses: the area swept by a wiper or a clock hand, a slice of a round cake or pizza, and the textbook "area of the shaded region" questions.
Questions
What is the formula for the area of a sector?
A = (θ ÷ 360°) × πr², or ½r²θ with θ in radians.
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc (a pizza slice). A segment is bounded by a chord and an arc.
How do I find the area of a segment?
Sector area minus the area of the triangle formed by the two radii and the chord: ½r²(θ − sin θ) in radians.
What area does a 15 cm minute hand sweep in 5 minutes?
The angle is 30°, so (30/360) × π × 15² ≈ 58.9 cm².
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.