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

Pitch diameter

Number of teeth

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

Outside diameter

Number of teeth

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

Base pitch

Pressure angle

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 

Number of teeth

Diametral pitch

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

Number of teeth

Outside 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 

Outside diameter

Diametral pitch

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 

Base diameter

Pressure angle

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

Number of teeth

Diametral pitch

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

Pitch diameter

Diametral pitch

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

Pitch diameter

Number of teeth

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 

Pitch diameter

Diametral pitch

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

Outside diameter

Diametral pitch

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 

C.D. between
both gears

Number of teeth
in each

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 

Pitch diameter

Pressure angle

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

Base diameter

Pitch diameter

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

Base pitch

Diametral pitch

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

Diametral pitch

Pressure angle

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