The formula to calculate Area of Circular Segment (A) is:
\[ A = \frac{(2 \cdot \angle Central) - \sin(\angle Central)}{4} \cdot \frac{lc^2}{2 - (2 \cdot \cos(\angle Central))} \]
Where:
The Area of Circular Segment is the total quantity of plane enclosed by the boundary of a Circular Segment.
The Central Angle of Circular Segment is the angle subtended by the arc of a Circular Segment with the center of the circle from which the Circular Segment is cut.
The Chord Length of Circular Segment is the length of the linear boundary edge of a Circular Segment.
Let's assume the following values:
Using the formula:
\[ A = \frac{(2 \cdot \angle Central) - \sin(\angle Central)}{4} \cdot \frac{lc^2}{2 - (2 \cdot \cos(\angle Central))} \]
Evaluating:
\[ A = \frac{(2 \cdot 3.1415926535892) - \sin(3.1415926535892)}{4} \cdot \frac{10^2}{2 - (2 \cdot \cos(3.1415926535892))} \]
The Area of Circular Segment is 39.2699081698613.
| Central Angle of Circular Segment (∠Central) | Chord Length of Circular Segment (lc) | Area of Circular Segment (A) |
|---|---|---|
| 3 | 9 | 29.809740498888154 |
| 3 | 9.5 | 33.213939259563652 |
| 3 | 10 | 36.802148764059446 |
| 3 | 10.5 | 40.574369012375541 |
| 3 | 11 | 44.530600004511932 |
| 3.1 | 9 | 31.190485437835065 |
| 3.1 | 9.5 | 34.752361861291540 |
| 3.1 | 10 | 38.506772145475388 |
| 3.1 | 10.5 | 42.453716290386616 |
| 3.1 | 11 | 46.593194296025224 |
| 3.2 | 9 | 32.723419484593911 |
| 3.2 | 9.5 | 36.460353191167911 |
| 3.2 | 10 | 40.399283314313472 |
| 3.2 | 10.5 | 44.540209854030607 |
| 3.2 | 11 | 48.883132810319303 |
| 3.3 | 9 | 34.426602066162353 |
| 3.3 | 9.5 | 38.358035018162376 |
| 3.3 | 10 | 42.501977859459686 |
| 3.3 | 10.5 | 46.858430590054311 |
| 3.3 | 11 | 51.427393209946231 |
| 3.4 | 9 | 36.321649027108066 |
| 3.4 | 9.5 | 40.469491662919786 |
| 3.4 | 10 | 44.841542008775392 |
| 3.4 | 10.5 | 49.437800064674867 |
| 3.4 | 11 | 54.258265830618221 |
| 3.5 | 9 | 38.434466760257990 |
| 3.5 | 9.5 | 42.823587964361529 |
| 3.5 | 10 | 47.449958963281468 |
| 3.5 | 10.5 | 52.313579757017820 |
| 3.5 | 11 | 57.414450345570579 |
| 3.6 | 9 | 40.796191450629358 |
| 3.6 | 9.5 | 45.455015782954312 |
| 3.6 | 10 | 50.365668457567104 |
| 3.6 | 10.5 | 55.528149474467732 |
| 3.6 | 11 | 60.942458833656197 |
| 3.7 | 9 | 43.444396704214597 |
| 3.7 | 9.5 | 48.405639537720575 |
| 3.7 | 10 | 53.635057659524186 |
| 3.7 | 10.5 | 59.132651069625418 |
| 3.7 | 11 | 64.898419768024269 |
| 3.8 | 9 | 46.424656677321629 |
| 3.8 | 9.5 | 51.726237841089841 |
| 3.8 | 10 | 57.314390959656336 |
| 3.8 | 10.5 | 63.189116033021108 |
| 3.8 | 11 | 69.350413061184156 |
| 3.9 | 9 | 49.792585811507180 |
| 3.9 | 9.5 | 55.478776166524980 |
| 3.9 | 10 | 61.472328162354550 |
| 3.9 | 10.5 | 67.773241798995883 |
| 3.9 | 11 | 74.381517076449001 |