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Segmented Bowl Ring Cuts

Calculate segment lengths and cutting angles for a regular polygonal wooden ring.

Formula & worked example
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Calculator inputs

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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

In initial display units, Number of segments 6, Outer ring diameter (Do) 20, Ring thickness (Tr) 2, Outer fudge factor (ao) 0, Inner fudge factor (ai) 0 gives Outer ring radius (Ro) 10, Inner ring diameter (Di) 16, Inner ring radius (Ri) 8, Cutting angle (α) 30, Interior angle (θ) 60.

Cutting angle = 180°/segments; outer length = 2(R+outer allowance)tan(π/segments); inner length = 2(r−inner allowance)sin(π/segments).

Worked example

Enter these known values and leave the other values blank.

Show additional ring dimensions: Display other parameters
Number of segments: 6 segments
Outer ring diameter (Do): 20 cm
Ring thickness (Tr): 2 cm
Outer fudge factor (ao): 0 cm
Inner fudge factor (ai): 0 cm

Interior angle (θ): 60 deg
Outer ring radius (Ro): 10 cm
Outer ring circumference (Co): 62.8 cm
Inner ring diameter (Di): 16 cm
Inner ring radius (Ri): 8 cm
Inner ring circumference (Ci): 50.3 cm
Segment's thickness (Ts): 3.07 cm
Segment's inner length (Li): 8 cm
Segment's outer length (Lo): 11.55 cm
Cutting angle (α): 30 deg

Assumptions and limitations

Segments must be a whole count of at least three. Both allowances are nonnegative; the inner allowance must be smaller than the inner radius. Kerf, glue gaps, grain orientation and machining accuracy are excluded.
Select compatible units and clear the quantity to solve before supplying the remaining measurements. Rounded purchase counts cannot uniquely recover a continuous dimension. Currency choices label amounts and do not convert exchange rates.

Common questions

How can I solve for a missing measurement?

Clear that field, then enter independent known values. Lock a known measurement to preserve it while changing another value. Procurement counts are rounded upward and cannot be reversed uniquely.

References

Enforce the stated physical and discrete input domains.

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