KEVOS® MAKEOS · Geometry
Circular Segment and Arc
What chord, arc length, angle and area does this circular segment have?
Solve a circular segment from its radius and height, or find the radius of an arc from a measured chord and height.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Known values | choice | Choose what you have measured or know from the drawing. |
| Radius | mm | Drawing radius (used only with radius and height). |
| Chord length | mm | Straight distance between the arc ends, measured or from the drawing (used only with chord and height). |
| Segment height (sagitta) | mm | Distance from the chord midpoint to the arc, at right angles to the chord. |
Method and formulas
- From chord c and height h: radius r = (c²/4 + h²) ÷ (2h).
- Included angle θ = 2 × arccos((r − h) ÷ r); chord = 2√(h(2r − h)); arc = r × θ (θ in radians).
- Segment area = r²(θ − sin θ) ÷ 2.
- Example: radius 50 mm and height 20 mm give a chord of 80 mm, an included angle of 106.26°, an arc of 92.73 mm and an area of 1,118.2 mm².
Limitations
- Assumes a true circular arc; a measured profile with form error gives an averaged radius.
- A small height relative to the chord makes the calculated radius very sensitive to the height measurement.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find the radius of a curved part from a chord and height measurement
- Lay out arcs, flats and partial bores
- Estimate area of a segment-shaped plate or liquid section
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- Radius
- Chord length
- Included angle
- Arc length
- Segment area
Interpreting the result
- Check the sensitivity table: when the height is small, a few micrometres change the radius considerably.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 77–80. Topic reference; no source tables or recommended settings are reproduced.
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 66–76. Topic reference; no source tables or recommended settings are reproduced.
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