How to use segmented turning ring layout
What this calculation does
A segmented-ring layout uses equal polygon segments to estimate each end miter and the inner and outer chord lengths before turning.
Measure radii to the segment vertices, enter the number of equal segments, and keep the inner radius smaller than the outer radius.
Enter the measurements
- Outer radius to segment vertices: Measure from the center to an outer segment vertex.
- Inner radius to segment vertices: Measure to an inner vertex of the same polygon.
- Equal segments in ring: Count equal pieces around the ring.
Formula and variables
End miter setting = 180° ÷ segment count. Chord at radius R = 2 × R × sin(π ÷ segment count); calculate once at the outer radius and once at the inner radius.
Each end miter is 180 degrees divided by segment count. Chord length is twice the radius times sine of pi divided by segment count.
Read the result
Twelve segments use a 15 degree end miter; the outer and inner chords are about 3.106 and 2.588 in.
Worked example
Inputs: 12 segments, 6 in outer vertex radius and 5 in inner vertex radius
- Miter = 180÷12 = 15°.
- Chord factor = 2sin(π÷12) ≈ 0.517638; 6×factor ≈ 3.106 in and 5×factor ≈ 2.588 in.
Expected result: 15° end miter; outer chord 3.106 in and inner chord 2.588 in
Frequently asked questions
Is the outer radius the finished circular diameter?
No. Enter radius to the polygon vertices before the ring is turned round.
Does this choose lathe speed or clamping?
No. It only calculates geometry; select and check the turning setup separately.
Conditions, presets and technical notes
Radii are measured to the polygon vertices before turning; this is not the finished circular outside diameter. Inner radius must be positive and less than outer radius. Turning allowance, glue joints, clamping, lathe speed and workholding are not calculated.