BIZOMAT MAKEOS · Gears
Spur Gear Dimensions (Diametral Pitch)
What are the diameters, tooth depth and centre distance of this inch (diametral pitch) spur gear pair?
Pitch, outside and root diameters, addendum, dedendum, whole depth, circular pitch, tooth thickness and centre distance of a diametral-pitch spur gear pair, with metric equivalents.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Diametral pitch | 1/in | Diametral pitch (teeth per inch of pitch diameter). |
| Pinion teeth | teeth | Pinion tooth count. |
| Gear teeth | teeth | Gear tooth count. |
| Tooth system | choice | Tooth proportions of the gear system. |
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: Diametral pitch
- What it is
- The diametral pitch: the number of teeth per inch of pitch diameter, the inch-system measure of tooth size.
- Units and format
- Enter a number in 1/in: threads per inch. The form accepts 0.000001 1/in to 200 1/in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 1/in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every diameter, the centre distance and the tooth depth fall in inverse proportion.
- Get it right
- A larger diametral pitch means smaller teeth, the opposite of the module.
What this means: Pinion teeth
- What it is
- The number of teeth on the pinion, the smaller gear of the pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Gear teeth
- What it is
- The number of teeth on the larger gear of the pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Tooth system
- What it is
- The tooth proportions the gears are cut to: full-depth or stub teeth and the pressure angle, which set the addendum and dedendum.
- Units and format
- Choose one of 3 options from the list: 20° full depth; 14½° full depth; 20° stub.
- Example
- The form opens with “20° full depth” selected as a worked example. Choose the option that matches your case.
- Get it right
- Both gears in a pair must use the same tooth system.
Method and formulas
- Pitch diameter = N ÷ P; addendum a = 1/P (stub 0.8/P).
- Dedendum b = 1.25/P (20° FD), 1.157/P (14½° FD), 1/P (stub); OD = (N + 2aP) ÷ P; root = PD − 2b.
- Circular pitch = π ÷ P; tooth thickness = π ÷ 2P; centre distance = (N₁ + N₂) ÷ 2P; module = 25.4 ÷ P.
- Example: 10 DP, 20 teeth: PD 2 in, OD 2.2 in, centre distance 3.25 in.
Limitations
- Standard proportions; fine-pitch gears (20 DP and finer) add a clearance allowance to the dedendum.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Machine or replace inch-system gears
- Convert diametral pitch to module
- Check gear blank diameters
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pitch, outside and root diameters
- Addendum, dedendum and whole depth
- Circular pitch and tooth thickness
- Centre distance and equivalent module
Interpreting the result
- Turn gear blanks to the outside diameter before cutting.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2140, 2249–2251. Topic reference; no source tables or recommended settings are reproduced.
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