Segmented turning-ring stock
Mistake: Using half the diameter difference as the whole stock width.
Fix: Include the polygon corner correction in the calculated radial stock width.
Calculators · Free
Segmented turning-ring stock
Plan regular polygon segment blanks around finished circular ring dimensions.
01Enter your values
Runs in your browserRuns offline in your browser. Once the page and required files have loaded, processing needs no internet.
02Segmented turning-ring stock
Runs in your browser
How it works
Plan regular polygon segment blanks around finished circular ring dimensions.
a = π/N; W = Rₒ − Rᵢ cos(a)
Equal trapezoidal segments for a regular flat ring. Allowance is radial on both finished surfaces. Inner blank radius must remain nonnegative. Inner corners, not just wall thickness, determine stock width. Kerf, glue gaps, machine calibration, grain strength and safe turning speed are excluded. Works offline after loading.
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Inputs are processed on this page and are never sent to a server.
About this tool
Use tool ↑Plan regular polygon segment blanks around finished circular ring dimensions.
Let outer blank apothem Ro=finished outer diameter/2+allowance, inner circle radius Ri=finished inner diameter/2−allowance, and a=π/segment count. Radial stock width is Ro−Ri×cos(a). Outer long point length is 2×Ro×tan(a); inner short length is 2×Ri×sin(a). Each end’s miter angle is 180°/segment count.
How to use it
- Enter your values
Finished outer diameter · Finished inner diameter · Equal segments · Radial machining allowance
- Calculate / generate
Plan regular polygon segment blanks around finished circular ring dimensions.
- Result
Required radial stock width: 31.487415 mm Outer long-point length: 54.661635 mm Inner short-point length: 37.787581 mm
Calculation method
- Let outer blank apothem Ro=finished outer diameter/2+allowance, inner circle radius Ri=finished inner diameter/2−allowance, and a=π/segment count.
- Radial stock width is Ro−Ri×cos(a).
- Outer long point length is 2×Ro×tan(a); inner short length is 2×Ri×sin(a).
- Each end’s miter angle is 180°/segment count.
a = π/N; W = Rₒ − Rᵢ cos(a)
Segmented turning-ring stock
- Finished outer diameter
- 200 mm
- Finished inner diameter
- 150 mm
- Equal segments
- 12
- Radial machining allowance
- 2 mm
Result
Required radial stock width: 31.487415 mm Outer long-point length: 54.661635 mm Inner short-point length: 37.787581 mm
Frequently asked questions
What does this result assume?
Equal trapezoidal segments for a regular flat ring. Allowance is radial on both finished surfaces. Inner blank radius must remain nonnegative. Inner corners, not just wall thickness, determine stock width. Kerf, glue gaps, machine calibration, grain strength and safe turning speed are excluded. Works offline after loading.
Where does my data go?
Calculations run on your device. Form inputs are not sent to a server.
Terms and definitions
Enter your values
- Measurement system
The initial choice follows your browser region. Your choice is remembered on this device. Gallons are US gallons. Switching units keeps your numbers unchanged and interprets them in the new unit.
Numbers stay unchanged. Check the new unit and enter the intended measurement, or select an example for that system.
- Finished outer diameter
Outside diameter of the final circular ring.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 1e-9 · Maximum: 1000000000000 mm
- Finished inner diameter
Inside diameter; must be smaller than the outer diameter.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 0 · Maximum: 1000000000000 mm
- Equal segments
Whole number of identical segments, at least three.
Enter a whole number; fractional counts are not valid.
Minimum: 3 · Maximum: 10000
- Radial machining allowance
Extra stock on each finished radial surface; not a diameter allowance.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 0 · Maximum: 1000000000000 mm
Result
- Result
Let outer blank apothem Ro=finished outer diameter/2+allowance, inner circle radius Ri=finished inner diameter/2−allowance, and a=π/segment count. Radial stock width is Ro−Ri×cos(a). Outer long point length is 2×Ro×tan(a); inner short length is 2×Ri×sin(a). Each end’s miter angle is 180°/segment count.
Calculated from your entries using the method below.
- Required radial stock width
Blank outer apothem minus inner polygon apothem.
Calculated from your entries using the method below.
- Outer long-point length
Long edge of each trapezoidal segment.
Calculated from your entries using the method below.
- Inner short-point length
Short edge of each trapezoidal segment.
Calculated from your entries using the method below.
- Value
Let outer blank apothem Ro=finished outer diameter/2+allowance, inner circle radius Ri=finished inner diameter/2−allowance, and a=π/segment count. Radial stock width is Ro−Ri×cos(a). Outer long point length is 2×Ro×tan(a); inner short length is 2×Ri×sin(a). Each end’s miter angle is 180°/segment count.
Calculated from your entries using the method below.
- Unit
Let outer blank apothem Ro=finished outer diameter/2+allowance, inner circle radius Ri=finished inner diameter/2−allowance, and a=π/segment count. Radial stock width is Ro−Ri×cos(a). Outer long point length is 2×Ro×tan(a); inner short length is 2×Ri×sin(a). Each end’s miter angle is 180°/segment count.
Calculated from your entries using the method below.
- End miter angle
Deviation from a square crosscut at each segment end.
Calculated from your entries using the method below.
Common mistakes and quick fixes
Limits and key assumptions
- Equal trapezoidal segments for a regular flat ring. Allowance is radial on both finished surfaces. Inner blank radius must remain nonnegative. Inner corners, not just wall thickness, determine stock width. Kerf, glue gaps, machine calibration, grain strength and safe turning speed are excluded. Works offline after loading.
- Displayed results may be rounded; rounding does not add measurement precision.