BIZOMAT MAKEOS · Power Transmission
Spur Gear Pair Geometry
What nominal geometry and speed ratio follow from module and tooth counts?
Calculate reference geometry and ideal output speed for an unshifted external spur gear pair.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Common transverse module of both spur gears. |
| Driver teeth | teeth | Tooth count of the input gear. |
| Driven teeth | teeth | Tooth count of the output gear. |
| Input speed | rpm | Speed of the driver. |
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: Module
- What it is
- The tooth size of the spur gears: reference (pitch) diameter divided by the number of teeth. Both gears in a pair must share the same module.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Reference diameters and centre distance are directly proportional to module; speeds do not change.
- Get it right
- Gears specified by diametral pitch (DP) use inches: module is 25.4 divided by DP.
What this means: Driver teeth
- What it is
- The number of teeth on the input gear, the one driven by the motor or upstream shaft.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 3 teeth to 10000 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.
- Effect on the result
- More driver teeth raise the output speed and the driver reference diameter.
- Get it right
- Count the teeth on the gear that receives the input speed, not the output.
What this means: Driven teeth
- What it is
- The number of teeth on the output gear that the driver meshes with.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 3 teeth to 10000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output speed is inversely proportional to driven teeth.
- Get it right
- For speed reduction the driven gear has more teeth than the driver.
What this means: Input speed
- What it is
- The rotational speed of the driver gear.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output speed is directly proportional to input speed.
- Get it right
- Use the speed at the driver gear’s shaft, after any belt or earlier stage.
Method and formulas
- Reference diameter = module × tooth count.
- Nominal centre distance = module × (driver teeth + driven teeth) / 2.
- Speed ratio = driven teeth / driver teeth; output RPM = input RPM / ratio.
- Example: module 2, 20/60 teeth gives 40/120 mm reference diameters, 80 mm centres and 400 rpm output from 1200 rpm.
Limitations
- External spur gears without profile shift; both must have compatible tooth system and pressure angle.
- No tooth-strength, undercut, backlash, contact ratio or lubrication rating.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- spur gear
- module
- gear ratio
Who it is for
- Mechanical designers
What you get
- Driver reference diameter
- Driven reference diameter
- Nominal centre distance
- Reduction ratio
- Output speed
Interpreting the result
- Confirm the manufacturer’s operating centre distance and all rating conditions before selecting gears.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2126–2133. Topic reference; no source tables or recommended settings are reproduced.
- KHK Gears: Calculation of Gear Dimensions — https://khkgears.net/new/gear_knowledge/gear_technical_reference/calculation_gear_dimensions.html
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