Circular Sector (Pie Slice) Area and Arc

The pie slice between two radii, and its arc - a curved patio or bed, a sprinkler coverage wedge, a gear or cam sector, or a fan of pavers. area = (1/2) r^2 theta = (angle/360) pi r^2, arc = r theta, chord = 2 r sin(theta/2). A 5 ft radius, 60-degree sector covers 13.1 ft^2 with a 5.24 ft curved edge and a 5.0 ft chord across the mouth (perimeter 15.24 ft); open it to 360 degrees for the full circle, 78.5 ft^2. The circular segment (the chord-and-arc region) and the cylindrical wedge are separate shapes. A shop and layout aid; verify critical dimensions on the work.

theta = angle x pi/180; area = (1/2) r^2 theta = (angle/360) pi r^2; arc = r theta; chord = 2 r sin(theta/2); perimeter = arc + 2 r.

The circular sector area (1/2) r^2 theta and arc length r theta - standard plane geometry as in Machinery's Handbook (Industrial Press), by name; public domain.

Pure plane geometry, public; the radius and central angle are user-supplied.

Estimate. AHJ and licensed professional govern.

Field names used by the API: radius, angle_deg, area, arc_length, chord

• Sector area/arc area = (1/2) r^2 theta, arc = r theta; the fraction angle/360 of the circleplane geometry
• Scope sector (two radii + arc); the segment (chord + arc) is separatescope of this tile