Radius and central angle
Circular arc & segment
Inputs
Nominal planar circle radius.
Angle subtended by the arc from greater than 0 through 360 degrees.
Results
Arc length
157.08
Chord length
129.9
Sector area
5,890.5
Circular-segment area
3,454.8
s = rθ; c = 2r sin(θ/2); Asector = r²θ/2; Asegment = Asector − r²sinθ/2
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Section geometry · Right-triangle frame · 3D coordinate span · Cylinder geometry
Method
Formula, when it applies, and when it does not
Calculate arc length, chord, sector area, and circular-segment area from radius and central angle.
s = rθ; c = 2r sin(θ/2); Asector = r²θ/2; Asegment = Asector − r²sinθ/2
When
- Planar circle
- Central angle from 0 to 360 degrees
- Nominal geometry
Don’t
- This is nominal planar-circle geometry. It excludes manufacturing tolerances, three-dimensional curvature, material thickness, bend allowance, forming response, and any manufacturing or inspection decision.
Elementary geometry — standard results