I am a novice who is trying to make some gears. I have followed the formula's but sadly something seems to go wrong and the gear's don't come out right. Below is some dimensions and pictures.

Gear 1

  • Module(Diametral Pitch)(P) = 3,

Teeth(N) = 12,

Pitch Diameter(PD) = 36,

Addendum(A) = MODULE = 3,

Deddendum(B) = 32.529,

Outside Diameter(OD) = 39,

Root Diameter(RD) = 28.5,

Base Circle(BC) = 33.82884,

Circular Pitch (CP) = 9.4248,

This produces a gear that looks "right" (small gear on right) here is a link to my CAD file https://cad.onshape.com/documents/e67e4eedf7e94a76c439bef0/w/4a5cb0732a0c5ca585fb5d87/e/2a98076fc77593239bb0eaa7

Now when i apply the same formula's to gear 2 i get a issue.

Gear 2

  • Module(Diametral Pitch)(P) = 3,

Teeth(N) = 40,

Pitch Diameter(PD) = 120,

Addendum(A) = MODULE = 3,

Deddendum(B) = 116.529,

Outside Diameter(OD) = 123,

Root Diameter(RD) = 112.5

Base Circle(BC) = 112.7628,

Circular Pitch (CP) = 9.4248,

Pressure Angle = 20 (for both gears)

Here is link to the CAD file https://cad.onshape.com/documents/e67e4eedf7e94a76c439bef0/w/4a5cb0732a0c5ca585fb5d87/e/2a98076fc77593239bb0eaa7

The base circle and root diameter are practically the same ?!

The gear teeth look different but i have used the same formula's for both gears.

Here are the formula's i have used, just in case there is a massive error!!!!

  • Module(Diametral Pitch)(P) = 3 (Saw this number used so stuck with it!)

Teeth(N) = 40, (Wanted to try a bigger number)

Pitch Diameter(PD) = 120, (Teeth x Module) (40 X 3)

Addendum(A) = MODULE = 3, (I hope this is true !)

Deddendum(B) = 116.529, (1.157 x P(Module) = 1.157 x 3 = 3.471 =120 - 3.471 )

Outside Diameter(OD) = 123, (Pitch diameter + Addendum)

Root Diameter(RD) = 112.5 (Pitch Diameter - (2.5 X Module) = 120 - 7.5)

Base Circle(BC) = 112.7628, (Pitch Diameter x COS (20pressure angle)

Circular Pitch (CP) = 9.4248, (PI x Module)

Here are some pictures

gear 1 and 2 close up meshing same picture but further out view of both gears

The diameters you can see on the pictures are in order from the top of the tooth to the centre:

Outside diameter, Pitch circle(pitch diameter), Base circle, Root diameter,

The images show the bigger gear with its base circle and root diameter practically on the same diameter. The smaller gear seems more in proportion

I set the Module(diametral pitch), which in this case is 3. I only used this number because I saw it used in a example Involving 12 and 24 teeth gears.

Does anyone think I should have change it as one gear is quite big (gear 1 is 12 teeth and gear 2 is 40 teeth) or is it just personally preference?

Did I use the module of 3 incorrectly for these gears?

I sadly forgot to mention in the original question the centre distance between the gears, which is 78mm. I am not sure if you would set the module (diametral pitch) based on the centre distance.

  • 1
    $\begingroup$ Check this : engineering.stackexchange.com/q/11905/10902 $\endgroup$
    – Solar Mike
    Commented Jun 23, 2018 at 0:45
  • 1
    $\begingroup$ Could you include pictures, as you indicated in the beginning of your question? I suspect not everyone will be willing to download CAD files. I, for one, can't do so from behind my workplace's firewall, but I can see and possibly diagnose from pictures. $\endgroup$
    – Rayanth
    Commented Jun 23, 2018 at 4:00
  • $\begingroup$ The base circle and root diameter will get close together the larger the gear gets (the more teeth it has) because the module doesn't change, therefor neither do the addendum or dedendum. As a component of the overall circle, the teeth are a much smaller percentage on a larger gear. Your math checks out on paper for me, but since I can't load the CAD files, I can't see what you're seeing. $\endgroup$
    – Rayanth
    Commented Jun 23, 2018 at 5:59

1 Answer 1


Firstly it is correct that the gears are not in proportion. For a pair of meshing gears the teeth on both need to be the same size ie you don't just scale a standard gear by some factor to get different diameters.

So as you have noticed, on a larger gear the pitch circle diameter and root diameter will be proportionally closer to each other than on a smaller gear.

This is what the Module number is for, its a ratio between the diameter and number of teeth.

It also looks like there is a problem resolving the tooth profiles. It looks like this may be an issue with the Addendum and Dedendum values you have used.

These are, conventionally the difference between the pitch circle diameter and the tip and root respectively ie addendum plus dedendum = the height of the tooth above the root circle.

The A and D values are what determines the overall shape the individual teeth

I think this may have confused your software and generated weird tooth profiles.


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