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

• Addendum

• Number of teeth

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

• Number of teeth

• Addendum

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

• Diametral pitch

Divide 1.5708 by the diametral pitch

t = 1.5708 / P_d

Addendum

• Diametral pitch

Divide 1 by the diametral pitch

a = 1 / P_d

Dedendum

• Diametral pitch

Divide 1.157 (or 1.25) by the diametral pitch

b = 1.157 / P_d

Working Depth

• Diametral pitch

Divide 2 by the diametral pitch

hk = 2 / P_d

Whole Depth

• Diametral pitch

Divide 2.157 (or 2.25) by the diametral pitch

ht = 2.157 / P_d

Clearance

• Diametral pitch

Divide .157 (or .250) by the diametral pitch

c = .157 / P_d

Clearance

• Diametral pitch

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

• Normal diametral pitch

• Number of teeth in both gears

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

• Operating diametral pitch

• Number of teeth in both gears

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)