Arc Radius from Chord & Sagitta
Arc Radius from Chord & Sagitta: calculate arc length with consistent units and explicit assumptions.
Inputs
mm
°
Results
- Radius
- 100 mm
- Central angle
- 90 °
- Arc length
- 157.079633 mm
- Chord
- 141.421356 mm
- Sagitta
- 29.289322 mm
- Sector area
- 7,853.981634 mm²
- Segment area
- 2,853.981634 mm²
Formula
Arc length = rθ; chord = 2r sin(θ/2)
Radius = chord²/(8 × sagitta) + sagitta/2
Off-center height = √(r²−x²) − (r−sagitta)
Assumptions & limits
- Angles may describe minor or major arcs; off-center mode uses a minor arc.
Worked example
For the example inputs: Radius = 100 mm; Central angle = 90 °; Arc length = 157.0796 mm.
Arc length = rθ; chord = 2r sin(θ/2)