Sector of a Circle Calculation

Calculator and formulas for calculating a circular sector

Circular Sector Calculator


On this page you can calculate the properties of a circular sector. A circle sector is a section of a circle. It is limited by two straight lines from its center.

To perform the calculation, enter the radius and the selected second parameter and then click the 'Calculate' button.


Circle sector calculator

 Input
Radius r
Decimal places
 Results
Angle α
Area A
Perimeter P
Arc b
Chord s
Centroid S
Height h
Keisausschnitt

Formulas for calculating sectors of a circle


Angle \(\displaystyle α = \frac{360 · A}{r^2·π}\)

\(\displaystyle α = \frac{180 · (P-2·r)}{r·π}\)

\(\displaystyle α = \frac{180 · b}{r·π}\)

\(\displaystyle α = 2 · asin\left( \frac{s}{2·r}\right)\)

Area   \(\displaystyle A = r^2 · π · \frac{α}{360°}\)
Arc length   \(\displaystyle b = r · π · \frac{α}{180°}\)
Perimeter   \(\displaystyle P = 2 · r + b\)
Chord   \(\displaystyle s = 2 · r · sin \left( \frac{α}{2}\right)\)
Centroid   \(\displaystyle S = \frac{2}{3} · \frac{r · s}{b} \)
Height   \(\displaystyle h = r-r\cdot sin\left(\frac{180-α}{2}\right) \)

\(\displaystyle h = r-\sqrt{r^2 -\frac{s^2}{4}} \)

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