How to use
- Enter radius.
- Choose angle unit.
- Enter central angle.
Formula
Degrees become radians with angle × π ÷ 180. Sector area is (1/2) × radius² × that radian angle. The full circle is π × radius². Arc length is the radian angle times the radius. The percent line is the sector divided by the full circle. Figures are rounded to four decimal places.
Worked example
The form opens at radius 10 and 60 degrees. The full circle is 314.1593. The sector is one sixth of that, 52.3599. The arc along the edge is 10.472. The percent of the circle is 16.6667%.
How to read the result
52.3599 is the pie-slice area, including the two straight radii and the arc. It is not the triangle alone and not the arc length. Doubling the radius multiplies the area by 4. Doubling the angle doubles the area.
When this does not apply
The slice must come from a circle, with the angle at the centre. A slice of an ellipse, or a piece whose tip is not the centre, uses a different area. The radius and the angle must describe the same circle.