Circle Sector Area Calculator
Find the area of a pie-slice sector of a circle from its radius and central angle, in degrees or radians.
units
Angle unit
Slice of the full circle
25%
of circleSector
25%
Rest of circle
75%
- 1
Convert angle to radians
θ = 90 × π ÷ 180 = 1.570796 - 2
Square the radius
r² = 5² = 25 - 3
Sector area A = ½ × r² × θ
½ × 25 × 1.570796 = 19.63
How does this calculator work?
A circular sector area equals one half the radius squared times the central angle in radians: A = ½ r² θ. Convert degrees to radians first (θ = deg × π/180). The sector is the fraction θ/(2π) of the whole circle (area π r²), and its arc length is r × θ.
Formula
How this is calculated
A circular sector is the pie-slice region bounded by two radii and the arc between them. Enter the radius r and the central angle. The angle unit selector lets you supply the angle in degrees or radians; degrees are converted with θ_rad = angle × π / 180, while radians are used directly.
The sector area is A = ½ × r² × θ, where θ must be in radians. This follows from the fact that a sector is the fraction θ / (2π) of the whole circle, and the whole circle has area π × r². Multiplying the fraction by π r² gives ½ r² θ. The donut chart visualizes exactly this fraction of the full circle, and the arc length is reported as s = r × θ.
Assumptions: the radius is a positive length and area is returned in squared length units (square units of whatever r uses). An angle of 0 gives zero area, a full turn (360° or 2π) gives the whole circle, and angles beyond a full turn are allowed mathematically but no longer correspond to a simple slice. A non-positive radius is rejected.
Frequently asked questions
The formula A = ½ r² θ assumes θ is in radians because radians directly express the arc fraction θ / (2π). If you have degrees, the calculator converts them first using θ_rad = degrees × π / 180.
A sector is the fraction θ / (2π) of the circle. Multiplying that fraction by the full area π r² gives the sector area, which simplifies to ½ r² θ.
The area is in squared units of the radius. If r is in centimeters, the area is in square centimeters; the tool labels it generically as square units.
Also known as
TG we-Calculate Editorial Team. (2026). Circle Sector Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sector-area-calculator
TG we-Calculate Editorial Team. "Circle Sector Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/sector-area-calculator.
TG we-Calculate Editorial Team, "Circle Sector Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sector-area-calculator
@misc{wecalculate_sector_area_calculator, title = {Circle Sector Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sector-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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