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Properties of a Circular area
Properties of a Semi-Circular area
Properties of a Circular Segment
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Properties of a Circular sector

- By Dr. Minas E. Lemonis, PhD - Updated: May 16, 2019

This tool calculates the basic geometric properties of a circular sector. Enter the shape dimensions R and φ below. The calculated results will have the same units as your input. Please use consistent units for any input.

R =
φ =
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Geometric properties:
Area =
Perimeter =
Arc length =
rc =
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Definitions

Geometry

The area A, the perimeter P and the arc length L of a circular sector, with radius R and central angle φ (in radians), can be found with these formulas:

\begin{split} A & = \frac{\varphi}{2} R^2 \\ P & = \left(\varphi+2\right) R \\ L & = \varphi R \end{split}

The centroid (center of gravity) of the circular sector is located along the bisector of the central angle φ, at a distance from the centre equal to:

r_c = \frac{4 r \sin{\frac{\varphi}{2}} }{3\varphi }

See also
Properties of a Circular area
Properties of a Semi-Circular area
Properties of a Circular Segment
All Geometric Shapes tools