BIZOMAT MAKEOS · Gears
Roller Chain Sprocket Diameters
What are the pitch, outside, bottom and caliper diameters of this sprocket?
Pitch diameter, approximate outside diameter, bottom diameter and caliper diameter (for odd tooth counts) of a roller chain sprocket from chain pitch, tooth count and roller diameter.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Chain pitch | mm | Chain pitch (15.875 mm for 10B/ANSI 50, 12.7 mm for 08B/ANSI 40). |
| Number of teeth | teeth | Tooth count of the sprocket. |
| Roller diameter | mm | Roller diameter of the chain from its data sheet. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Chain pitch
- What it is
- The roller chain pitch: the distance between the centres of neighbouring rollers along the chain.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15.875 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All sprocket diameters scale in proportion to the pitch.
- Get it right
- Take it from the chain designation or data sheet; it is not the roller diameter.
What this means: Number of teeth
- What it is
- The number of teeth around the sprocket that engage the chain rollers, counted on the actual sprocket or taken from its catalogue designation.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 500 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 17 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth give a larger pitch diameter.
- Get it right
- Odd and even counts are measured differently; the tool gives a caliper diameter for odd counts.
What this means: Roller diameter
- What it is
- The diameter of the chain’s rollers, from the chain data sheet; it is subtracted from the pitch diameter to give the bottom diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.16 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the roller diameter, not the pin or bush diameter.
Method and formulas
- Pitch diameter = p ÷ sin(180° ÷ N).
- Bottom diameter = PD − roller diameter.
- Caliper diameter (odd N) = PD cos(90° ÷ N) − roller diameter; outside diameter ≈ p (0.6 + cot(180° ÷ N)).
- Example: 17 teeth on 15.875 mm pitch: PD 86.395 mm, bottom 76.235 mm.
Limitations
- The outside diameter is the ANSI approximate value; tooth form tolerances come from the chain standard.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Machine or inspect sprockets
- Check clearances around a sprocket
- Measure worn sprockets
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pitch diameter
- Approximate outside diameter
- Bottom diameter
- Caliper diameter (odd teeth)
Interpreting the result
- Measure worn sprockets across the bottoms (or caliper for odd teeth) and compare with these values.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2537–2550. Topic reference; no source tables or recommended settings are reproduced.
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