Sector of a Circle Calculation
Calculator and formulas for calculating a circular sector
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.
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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 |
\(\displaystyle h = r-r\cdot sin\left(\frac{180-α}{2}\right) \) \(\displaystyle h = r-\sqrt{r^2 -\frac{s^2}{4}} \) |
Angle functions
From Deg, Min, Sec to Decimal • From Degree to Percent • Angle sum • Side lengths from anglesCircular functions
Annulus • Annulus sector • Circle • Circular angles • Circular arcs • Circular sector • Circular segment • Ellipse • Parabolic arch • Squaring the Circle
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