To Get 
Having 
Rule 
Formula 
Diametral Pitch 
The circular pitch 
Divide 3.1416 by the circular
pitch 
P_{d} =
3.1416 / CP 
Diametral Pitch 

Divide the number of teeth by the
pitch diameter 
P_{d} =
N / D 
Diametral Pitch 

Divide number of teeth + 2 by the
outside diameter 
P_{d} =
(N+2) / OD 
Diametral Pitch 

Divide the base pitch by the
cosine of the pressure angle then divide by 3.1416 
P_{d} =
(BP / Cos PA) / 3.1416 
Pitch Diameter 

Divide the number of teeth by the diametral pitch 
D
= N / P_{d} 
Pitch Diameter 

Divide the product of the outside
diameter + number of teeth by the number of teeth + 2 
D
= (OD x N) / (N+2) 
Pitch Diameter 

Subtract 2 divided by the diametral pitch from the outside diameter 
D
= OD  (2/ P_{d}) 
Pitch Diameter 

Multiply addendum by the number of
teeth 
D
= A x N 
Pitch Diameter 

Divide the base diameter by the
cosine of the pressure angle 
D
= BD / (Cos Pa) 
Outside Diameter 

Divide number of teeth + 2 by the diametral pitch 
OD
= (N+2) / P_{d} 
Outside Diameter 

Two divided by the diametral pitch plus pitch diameter 
OD
= (2 / P_{d}) + D 
Outside Diameter 

Number of teeth + 2, divided by
the quotient of number of teeth divided by the pitch diameter 
OD
= (N+2) / (N / D) 
Outside Diameter 

Multiply the number of teeth + 2
by the addendum 
OD
= (N + 2) x A 
Number Of
Teeth 

Multiply the pitch diameter by the
diametral pitch 
N
= D x P_{d} 
Number Of
Teeth 

Multiply the outside diameter by
the diametral pitch and subtract 2 
N
= (OD x P_{d})  2 
Thickness Of
Tooth 

Divide 1.5708 by the diametral pitch 
t
= 1.5708 / P_{d} 
Addendum 

Divide 1 by the diametral pitch 
a
= 1 / P_{d} 
Dedendum 

Divide 1.157 (or 1.25) by the diametral pitch 
b
= 1.157 / P_{d} 
Working Depth 

Divide 2 by the diametral pitch 
hk = 2 / P_{d} 
Whole Depth 

Divide 2.157 (or 2.25) by the diametral pitch 
ht = 2.157 / P_{d} 
Clearance 

Divide .157 (or .250) by the diametral pitch 
c
= .157 / P_{d} 
Clearance 

Divide thickness of tooth at the pitchline by 10 
c
= t / 10 
Operating Diametral
Pitch 

Add the number of teeth in both
gears and divide by 2 then divide by the center distance 
P_{dO} =
((n1 + n2)/2) / C 
Center Distance 

Add the number of teeth in both
gears and divide by 2 then divide by the normal diametral
pitch 
C
= ((n1 + n2)/2) / P_{nd} 
Operating Center Distance 

Add the number of teeth in both
gears and divide by 2 then divide by the operating diametral
pitch 
Co
= ((n1 + n2)/2) / P_{od} 
Base Diameter 

Multiply the pitch diameter by the
cosine of the pressure angle 
Db
= PD x (cos PA) 
Pressure Angle 

Divide the base diameter by the
pitch diameter 
cosPA
= Db / D 
Pressure Angle 

Divide Pi by the diametral pitch, then divide by the base pitch 
cosPA
= (3.1416 / P_{d}) / Pb 
Base Pitch 

Divide the diametral
pitch by Pi, then multiply by the cosine of the pressure angle 
Pb = (P_{d} / 3.1416) x (cos PA) 
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