How this calculator works
A ring of N pieces has a turn of 360/N degrees at each joint. Each cut supplies half that turn. Segment face lengths come from tangent geometry at the inner and outer apothems. The optional radial allowance enlarges the outer blank and shrinks the inner opening.
Formula
m = pi/N; long edge = 2(Ro+a) tan(m); short edge = 2(Ri-a) tan(m); strip width = Ro-Ri+2a; outside corner diameter = 2(Ro+a)/cos(m).
Worked example
A 12-segment ring with 300 mm outer and 200 mm inner diameters and no allowance uses 15 degree cuts, 80.3848 mm long edges, 53.5898 mm short edges and a 50 mm strip.
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Frequently asked questions
Why is the corner diameter larger?
The corners lie beyond the outer flats. Leave enough stock and lathe clearance for that larger blank.
Is layer height calculated?
No. Layer height is the stock thickness perpendicular to this flat ring and can be chosen separately.
Can I enter a cutting angle instead of a count?
Yes, when it corresponds to a whole number of segments that closes the ring.