# How to work out diameter of chainring from the number of teeth?

##### Squid
This may be a silly question, but is there some known way how to figure out the diameter of a chainring given how many teeth it has? I have a bashguard I recently installed on my bike replacing the 44T, but I noticed there is still some room between the bashguard and the 32T... And I don't know what diameter a 34T and 36T chainring would be. Ideally the 36T would be better, as long as it fits... if not I will have to settle for the 34T. But I need to know the diameter #### RCOH

##### Eats Squid
You could measure the distance between 2 teeth of a chainwheel (eg tip of 1 tooth to tip of next tooth), multiply distance by amount of teeth on any given chainwheel then use an equation involving pi to figure out diameter of any chainring.

C=pi*d

##### Squid
Thats not a bad idea actually, since the distance between teeth im guessing has to be exactly the same on all size chainrings, since links on chains are spaced by a certain distance...

Only thing I'm worried about is precision... Don't think I can measure the distance between 2 teeth precisely enough to give a good size calculation ##### Squid
OK so I took some measurements... As far as I can tell the distance between teeth on a chainring is 13mm. Using that measurement I get the following diameters...

28T = 116mm
32T = 132mm
34T = 141mm
36T = 149mm
38T = 157mm
44T = 182mm
48T = 199mm

Is anyone able to shed some light on how close these figures are to a "real" chainring? Unfortunately I cannot take a very accurate measurement of the ones I have access to as they are still on the bike... Last edited:

#### tu plang

##### knob
chain links are 1" long so the tooth pitch on a ring is going to be 12.7mm.

##### Squid
chain links are 1" long so the tooth pitch on a ring is going to be 12.7mm.
I wonder if the circular nature of a chainring though means that the distance from the teeth tips is more than what you would expect (12.7mm)?

#### tu plang

##### knob
if you want to be more accurate http://www.engineersedge.com/gear_formula.htm
has all the formulas you'd need... i did have the specific ones with diagrams at home... but not being at home i cant help... work your way through it ##### Squid
Thanks for the link but I'm confused... How do I use these formulas to figure out what I need?

I'm guessing the one I want is OD (outside diameter) which requires you to know N (number of teeth) and Diametric Pitch (P). Number of teeth is no problem we know that. But we don't know Diametric Pitch. So lets take a look at the formula on how to figure out P (Diametric Pitch).

There are 3 different ones.

One requires you to know the OD, which is what we are trying to figure out so thats obviously out.

Another one requires you to know the Pitch Diameter, so I take a look at how to figure out Pitch Diameter.... You need to know the Diametric Pitch!!! So that one is out.

That leaves the middle one, where you can figure out the Diametric Pitch by dividing pi by the Circular Pitch. We don't know the Circular Pitch so lets look up the formula for that...

Circular Pitch only has one formula... CP = pi/DP!!!! You divide pi by the Diametric Pitch to get the Circular Pitch! But we are trying to figure out the Diametric Pitch!

I'm confused, these formulas just go around in circles... Its like trying to figure out what X is in the formula X = Y * Z, not knowing what Y is, looking up the formula for Y and being told that Y = X / Z... !!!! #### tu plang

##### knob
hhaha yeah, i didnt really pay too much attention to what was on there... just assumed it was what i was looking for... but yeah do a search on google and you'll find something. if you can wait a week i can find the stuff at home.

otherwise, given the number of teeth of the chainrings in question, the polygon formed by estimating the circumference by adding up the tooth pitch is approaching a circle so it will be relatively accurate.

#### Jon

##### Not Grip, OK... So don't ask!
OK so I took some measurements... As far as I can tell the distance between teeth on a chainring is 13mm. Using that measurement I get the following diameters...

28T = 116mm
32T = 132mm
34T = 141mm
36T = 149mm
38T = 157mm
44T = 182mm
48T = 199mm

Is anyone able to shed some light on how close these figures are to a "real" chainring? Unfortunately I cannot take a very accurate measurement of the ones I have access to as they are still on the bike... Your calcs are spot on ,I have a race face 38t and its 157mm tooth tip to tooth tip .Try saying that 5 times fast cheers jon

Hey thanks for checking that for me, maybe my formula is pretty accurate after all 