Circular Sector

Portion of a circle enclosed between two radii.

Formulas

To calculate the area A in degrees: A = [latex]\dfrac{α}{360}[/latex] × πr[latex]^{2}[/latex]
To calculate the area A in radians: A = [latex]\dfrac{αr^{2}}{2}[/latex]

secteur circulaire

Examples

For a sector whose angle α is 90° (or π2 in radians) and whose radius r measures 10 cm, we have:

In degrees: [latex] A = \dfrac{a}{360} × π r^{2}= \dfrac{90}{360} × 100π = 25π[/latex].
In radians: [latex]A = \dfrac{αr^{2}}{2} = \dfrac{\dfrac{π}{2} × 10^{2}}{2} = 25π[/latex].