A unit of metric measurement indicating the size of the pitch of a gear.
It relates to the ratio of the pitch diameter to the number of teeth, thus the module of a gear = pitch diameter (in millimetres) divided by the number of teeth in the gear.
Module pitch is an actual dimension, whereas Diametral Pitch is only a ratio.
Normal Module: This is the value of the module in the Normal Plane, usually measured on the pitch line. see diagram. The calculation of the normal module is shown below.
Transverse Module: This is the value of the module in the Transverse Plane, usually measured on the pitch line. See diagram. The calculation of the transverse module is shown below.

Whereas:
From Gear data
z = number of teeth in gear (61)
M_n = normal module (8)
PD = pitch diameter of gear (488mm)
OD = outside diameter of gear (504mm)
ß = helix angle (15)

Calculated

Formula:
Normal Module: M_n - Known - Pitch diameter, Number of teeth in gear
= PD/z
= 488/61
= 8 normal module

Normal Module: M_n - Known - Outside diameter, Number of teeth in gear
= OD/(z+2)
= 504/(61+2)
= 504/63
= 8 normal module

Transverse Module: M_t - Known - normal module, helix angle
= M_n/cos(ß)
= 8/COs(15)
= 8/0.9659258
= 8.2822097 transverse module

Transverse Module: M_t - Known - Pitch diameter, Number of teeth in gear, Helix angle
= (PD/z)/COs(ß)
= (488/61)/COs(15)
= 8/0.965925
= 8.2822097 transverse module

Transverse Module: M_t - Known - Outside diameter, Number of teeth, Helix angle
= (OD/(z+2))/COs(ß)
= (504/(61+2))/COs(15)
= (504/63)/0.965925
= 8/0.965925
= 8.2822097 transverse module