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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