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Gear module is pitch diameter divided by tooth count and sets tooth size.
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Formula
m and d in mm (usual convention); z dimensionless
| Symbol | Meaning | Unit |
|---|---|---|
| Gear module | mm | |
| Pitch diameter | mm | |
| Number of teeth | dimensionless |
m=\frac{d}{z}For metric spur gears, module is a common size parameter; properly meshing standard gears need compatible module and reference profile. This definition alone says nothing about tooth-root strength or load capacity. It is usually stated in millimetres although d/z is formally a length in any consistent unit. No standard series or specific tooth geometry is prescribed here.
For metric spur gears, module is a common size parameter; properly meshing standard gears need compatible module and reference profile. This definition alone says nothing about tooth-root strength or load capacity. It is usually stated in millimetres although d/z is formally a length in any consistent unit. No standard series or specific tooth geometry is prescribed here.
Gear module is pitch diameter divided by tooth count and sets tooth size.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Module of a spur gear” and check its unit and magnitude.
A gear with pitch diameter d=80 mm and z=40 teeth has module m=2 mm.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: m and d in mm (usual convention); z dimensionless.
Formula cluster
Gear module is pitch diameter divided by tooth count and sets tooth size.
A gear with pitch diameter d=80 mm and z=40 teeth has module m=2 mm.
Describe gear size and compatibility of metric spur gears.
Here is how to work through a typical Module of a spur gear (m = d/z) task step by step:
Task
Work through the numerical example for “Module of a spur gear” and check its unit and magnitude.
Solution path
A gear with pitch diameter d=80 mm and z=40 teeth has module m=2 mm.
Module scales the tooth size of a metric spur gear. Gears with the same module have matching pitch, while more teeth give a larger pitch diameter. Module alone does not specify tooth shape or load capacity; additional geometry and material data are required. Module is a metric tooth-size parameter based on pitch diameter and tooth count. Use millimetres consistently with common gear catalogs. Matching module is necessary but not sufficient for meshing; pressure angle, tooth system, profile shift and center distance matter too.
Equal module is an important compatibility condition for metric spur gears but is not sufficient. Reference profile and pressure angle must also match; profile shift matters for special designs. Incompatible gears can mesh poorly, become noisy and wear faster despite equal m. Module is a metric tooth-size parameter based on pitch diameter and tooth count. Use millimetres consistently with common gear catalogs. Matching module is necessary but not sufficient for meshing; pressure angle, tooth system, profile shift and center distance matter too.
Module is a length, and metric gears usually use millimetres because common pitch diameters and tooth pitches give convenient values. If d is entered in metres, m is returned in metres and must be converted carefully. Mixing d units with the intended module unit can cause a factor-of-1000 error. Module is a metric tooth-size parameter based on pitch diameter and tooth count. Use millimetres consistently with common gear catalogs. Matching module is necessary but not sufficient for meshing; pressure angle, tooth system, profile shift and center distance matter too.
Write the quantity and unit from the variable list next to every value: m and d in mm (usual convention); z dimensionless. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A gear with pitch diameter d=80 mm and z=40 teeth has module m=2 mm. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Module is a metric tooth-size parameter based on pitch diameter and tooth count. Use millimetres consistently with common gear catalogs. Matching module is necessary but not sufficient for meshing; pressure angle, tooth system, profile shift and center distance matter too.
The background states this starting condition: For metric spur gears, module is a common size parameter; properly meshing standard gears need compatible module and. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Module is a metric tooth-size parameter based on pitch diameter and tooth count. Use millimetres consistently with common gear catalogs. Matching module is necessary but not sufficient for meshing; pressure angle, tooth system, profile shift and center distance matter too.
Quanta exam set
Curated exam set for "Module of a spur gear":
Question (front)
Which formula describes Module of a spur gear?
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Question (front)
How do you rearrange Module of a spur gear for Base equation for the target quantity?
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Question (front)
Which common mistake happens with Module of a spur gear?
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Create a curated FSRS exam set for m = d/z: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
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