Circle Sector Calculator
Find the area, arc length and perimeter of a pie-slice sector from its radius and central angle.
units
degrees
That is 25% of the full circle
25%
of circleSector area
25%
Rest of circle
75%
- 1
Angle to radians
90 × π ÷ 180 = —Sector formulas require radians. - 2
Sector area
½ × 5² × — = 19.63
How does this calculator work?
A circular sector is a pie slice set by radius r and central angle θ. Convert the angle to radians, then area = ½·r²·θ, arc length = r·θ, and perimeter = arc + 2r. The sector is the θ/360 fraction of the whole circle, and the result uses the same units as r (squared for area).
Formula
How this is calculated
A circular sector is the "pie slice" region bounded by two radii and the arc between them. You supply the radius r and the central angle θ measured in degrees. The angle is first converted to radians with θ_rad = θ · π / 180, because the standard sector formulas assume radian measure.
The sector area is ½ · r² · θ_rad, which is simply the fraction θ/360 of the full circle area πr². The arc length (the curved edge) is L = r · θ_rad, and the perimeter adds the two straight radii: P = L + 2r. The donut chart compares the sector area against the rest of the disk so you can see what slice of the whole circle it represents.
Radius and angle must be positive, and the result shares whatever linear unit you use for r (area is in those units squared). Angles above 360° wrap past a full revolution, so keep θ between 0 and 360 for a single, non-overlapping sector.
Frequently asked questions
Convert the central angle to radians (θ_rad = θ · π / 180), then multiply by the radius: arc length = r · θ_rad. For a 90° sector with r = 5, the arc is 5 · (π/2) ≈ 7.85 units.
The sector is the full pie slice bounded by two radii and the arc. A segment is the smaller region between the arc and the chord connecting the two radius endpoints, so the segment area equals the sector area minus the triangle formed by the two radii.
Yes. The sector perimeter is the curved arc plus both straight radii: P = r · θ_rad + 2r. It is not just the arc length.
Also known as
TG we-Calculate Editorial Team. (2026). Circle Sector Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/circle-sector-calculator
TG we-Calculate Editorial Team. "Circle Sector Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/circle-sector-calculator.
TG we-Calculate Editorial Team, "Circle Sector Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/circle-sector-calculator
@misc{wecalculate_circle_sector_calculator, title = {Circle Sector Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/circle-sector-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?