Spur Gear Terminology & Formulas | Pitch Diameter, Pressure Angle, Module

Spur Gear Terminology & Formulas 

What is a Spur Gear?

spur gear cold rolled

A spur gear is one of the simplest and most common types of cylindrical gears. Spur gears have straight teeth that run parallel to the shaft.

These gears are easy to manufacture and can be used in a variety of applications. These applications include speed increase or reduction, torque multiplication, and enhancing accuracy for positioning systems.

In this blog, we are going to define spur gear terminology and provide formulas for determining the values of these terms.

Spur Gears – Terms, Definitions, and Calculations

The following terms are related to spur gears:

  • Addendum: The height of the tooth above the pitch circle.
  • Backlash: The clearance between two mating teeth of separate gears.
  • Base circle: A theoretical circle used to generate the involute curve when creating tooth profiles.
  • Center distance: The distance between the center shafts of two gears.
  • Chordal addendum: The distance between a chord, passing through the points where
  • the pitch circle crosses the tooth profile and the tooth top.
  • Chordal thickness: Tooth thickness measured along a chord passing through the points where the pitch circle crosses the tooth profile.
  • Circular pitch: Measurement of the pitch circle arc length from one point on a tooth to the same point on the adjacent tooth.
  • Circular thickness: The thickness of the tooth at the pitch circle.
  • Clearance: The space between one gears minor diameter and the mating gears major diameter.
  • Dedendum: Depth of the tooth between the pitch circle and the minor diameter.
  • Diametral pitch: The number of teeth per inch of pitch diameter.
  • Fillet: The small radius that connects the tooth profile to the root circle.
  • Module: Teeth per millimeter of pitch diameter.
  • Outside diameter: The major diameter of the gear.
  • Pinion: The smaller-sized gear in any meshed pair.
  • Pitch circle: The circle, the radius of which is equal to the distance from the center of the gear to the pitch point. This is where the gear’s speed is measured.
  • Pitch diameter: Diameter of the pitch circle.
  • Pitch point: The point of tangency of the pitch circles of a pair of mating gears.
  • Pressure angle: The angle between the line of action and a line perpendicular to the line of centers.

Gear Pressure Angle Comparison - 14.5° & 20° - Grob Inc.

  • Root (or dedendum) circle: The minor diameter of the tooth.
  • Velocity ratio: Ratio of input gear revolutions to output gear revolutions within a specified amount of time.
  • Whole depth: The height of the tooth from major diameter to minor diameter of a gear.
  • Working Depth: The depth to which a tooth extends into the space between teeth on the mating gear.


Formulas for determining some of these terms include:

Addendum 1.0 ÷ diametral pitch
Clearance 0.157 ÷ diametral pitch
Diametral Pitch Number of teeth ÷ pitch diameter
Number of Teeth Pitch diameter * diametral pitch
Outside Diameter (Number of teeth + 2) ÷ diametral pitch
Pitch Diameter Number of teeth ÷ diametral pitch
Tooth Thickness 1.5708 ÷ diametral pitch
Whole Depth 2.157 ÷ diametral pitch
Working Depth 2 ÷ diametral pitch


Reverse Engineering Spur Gears

We often get asked how to reverse engineer spur gears and if we possess the capabilities to do it. The answer is yes, we can reverse engineer customer samples. We use a coordinate measuring machine (CMM) in conjunction with specialized gear software to determine the exact parameters of a given spur gear.

While it is possible to reverse engineer a spur gear using simple measuring tools and some quick math, this method can only be used on standard gears. Many times, a gear will be custom made for the application and certain dimensions or tolerances will be modified. Therefore using a CMM or a dedicated gear checker is necessary to determine a gear’s true parameters. For information on this process, visit our guide on reverse engineering spur gears.

Manufacturing the Gear You Need at Grob

spur gearsAt Grob, we can create cold rolled spur gears that meet the exact specifications for your project. Our standard gears are available in mild-to-medium carbon steel or aluminum, and they are available in either 14.5° or 20° pressure angles.

We are a family-owned-and-operated company that has been in business for 90 years and we have 60 technicians and engineers on staff at our manufacturing facility and headquarters located in Grafton, Wisconsin. We possess the experience and skills needed to produce quality products within your project deadline.

For more information about our gear manufacturing capabilities, please contact us.

By |2019-06-03T13:34:47+00:00May 21st, 2019|Uncategorized|Comments Off on Spur Gear Terminology & Formulas | Pitch Diameter, Pressure Angle, Module