Here are some formulas and definitions that might assist you in your gear calculations. Here is a picture worth a thousand words.
| Pitch Diameter | d |
| Pressure Angle | Phi |
| Number of teeth | N |
| Circular Pitch | Pc = Pi*d/N |
| Base Pitch | Pb = Pc*cos(Phi) |
| Diametral Pitch | Pd = N/d or Pi/Pc |
| Module | m = d/N |
| Addendum | a = 1/Pd |
| Dedendum | b = 1.25/Pd |
Gear terms & definitions
Addendum: The distance from the pitch circle to the tip of the gear tooth. For a spur, helical and worm gear it is taken on the radial line.
Addendum circle: Another term for the outside diameter of a spur or helical gear.
Addendum coefficient: The displacement, from the pitch circle of the gear, of that plane in the basic crown on which the tooth thickness is equal to half the circular pitch. It is expressed as a fraction of the module.
Axial thickness: the distance between the opposite faces of the same tooth or thread measured on the pitch cylinder in a direction parallel to the axis.
Backlash: The free movement at the pitch circle of one gear in the direction of the circumference. The other gear is fixed and no allowance is given for bearing clearance.
Base circle: circle from which the involute is developed.
Base pitch: The length of the line of action between the same faces of adjacent teeth, or base pitch equals the circumference of the base circle divided by the number of teeth in the gear.
Centre distance: The perpendicular distance between the axes of gears.
Circular pitch: Distance measuring along the pitch circle between the centres of two adjacent teeth. It may be given, as the circular pitch is the length of arc on the pitch circle between two similar faces of successive teeth measuring on a plane at right angles to the axis of rotation.
Clearance: The distance from the tip of the tooth to the circle passing through the bottom of the tooth space with the gears in mesh and measuring radially.
Constant cord: The cord between two points on the tooth profile which makes contact with the basic rack. For a given pitch and pressure angle the position and length for a standard tooth are constant.
Contact ratio: Ratio of the arc of action to the circular pitch.
Dedendum: The radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.
Diametral pitch: Ratio expressing the size of a gear tooth. It is equal to the number of teeth divided by the pitch diameter. Unless otherwise stated it is always used in English units.
Gear ratio: Ratio for a pair of spur or bevel gears is equal to that of teeth in the respective gears. It is the same for helical gears with shafts parallel and identical helix angles.
Line of action: For an involute tooth form is the common tangent to the base circles and passes through the pitch point of any pair of mating gears.
Module: Term used to denote tooth size. It is the pitch diameter divided by the number of teeth; hence it is the reciprocal of the diametral pitch.
Outside diameter: The distance measuring the tip to tip on the teeth.
Pitch, base: Pitch measured on the base circle, or along the line of action. The base pitch is a constant and fundamental distance between the teeth measuring along a common normal in the plane of rotation.
Pitch circle: The transverse section of the pitch cylinder normal to the axis.
Pitch, circular: The distance measuring along the pitch circle between the centres of two adjacent teeth on a plane at right angles to the axis of rotation.
Pitch, diametral: Ratio expressing the size of the gear teeth. It is equal to the number of teeth divided by the pitch diameter.
Pitch line of a rack: The imaginary pitch line associated with a rack; corresponds to the pitch circle of a spur or helical gear.
Pitch point: Point of contact and tangency of the two pitch circles. Unless specified the pressure angle is assumed to be the standard angle, taken at the pitch or reference diameter.
Pressure angle: The acute angle between the line of action, which is normal to the tooth surface, and the common tangent to the pitch circle at the pitch point.
Rack: The term given to teeth cut on a flat surface. As there is no curvature on the pitch line, teeth cut to a basic involute tooth form have straight sides. The teeth may be cut at right angles to the direction of travel as for a spur gear, or inclined if to mesh with a helical gear.
Teeth involute: When teeth of spur, helical, or worm gears, have, in the transverse plane, the active portion of the profile forming an involute off a circle.
Tooth thickness: The length of arc measured along the pitch circle between the opposite faces of the same tooth.