Gear Module Calculator
Calculate gear module, pitch diameter, and center distance from tooth count and module. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Pitch Diameter = Module x Number of Teeth | Center Distance = m(z1 + z2) / 2
Module (m) is the ratio of pitch diameter to tooth count in millimeters. Pitch diameter d = m x z. Center distance a = m(z1 + z2)/2. Addendum = m, Dedendum = 1.25m. Circular pitch p = pi x m. These relationships define all standard tooth proportions.
Worked Examples
Example 1: Standard Spur Gear Pair Design
Problem:Design a gear pair with module 3 mm, 18-tooth pinion, 45-tooth gear, and 20-degree pressure angle. Calculate key dimensions.
Solution:Pitch diameter (pinion) = m x z1 = 3 x 18 = 54 mm\nPitch diameter (gear) = m x z2 = 3 x 45 = 135 mm\nCenter distance = (54 + 135) / 2 = 94.5 mm\nCircular pitch = pi x 3 = 9.425 mm\nAddendum = m = 3 mm\nDedendum = 1.25m = 3.75 mm\nOuter dia (pinion) = 54 + 6 = 60 mm\nOuter dia (gear) = 135 + 6 = 141 mm\nGear ratio = 45/18 = 2.5:1
Result:Center Distance: 94.5 mm | Gear Ratio: 2.5:1 | Circular Pitch: 9.425 mm
Example 2: Module Selection for Speed Reducer
Problem:A speed reducer needs a 4:1 ratio with 20-tooth pinion. Determine dimensions for module 2.5 mm.
Solution:Gear teeth = 20 x 4 = 80 teeth\nPitch dia (pinion) = 2.5 x 20 = 50 mm\nPitch dia (gear) = 2.5 x 80 = 200 mm\nCenter distance = (50 + 200) / 2 = 125 mm\nAddendum = 2.5 mm, Dedendum = 3.125 mm\nOuter dia (pinion) = 50 + 5 = 55 mm\nOuter dia (gear) = 200 + 5 = 205 mm\nBase dia (pinion) = 50 x cos(20) = 46.985 mm
Result:Center Distance: 125 mm | Pinion OD: 55 mm | Gear OD: 205 mm
Frequently Asked Questions
What is gear module and why is it important in gear design?
Gear module is the fundamental parameter that defines the size of gear teeth in the metric system. It is calculated as the ratio of the pitch diameter to the number of teeth, expressed in millimeters. The module determines all other tooth dimensions including addendum, dedendum, tooth thickness, and clearance. Two gears must have the same module to mesh properly, making it the primary compatibility parameter in gear design. Standard module values follow ISO 54 and include sizes like 0.5, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, and larger. Selecting the correct module ensures adequate tooth strength while maintaining compact gear dimensions for the required power transmission.
What is the difference between module and diametral pitch?
Module and diametral pitch are reciprocal measures of gear tooth size used in different measurement systems. Module is the metric standard expressed in millimeters, calculated as pitch diameter divided by the number of teeth. Diametral pitch is the imperial standard expressed in teeth per inch, calculated as the number of teeth divided by pitch diameter in inches. The conversion relationship is diametral pitch equals 25.4 divided by module. For example, a module 2 gear has a diametral pitch of 12.7. Engineers working on international projects must be fluent in both systems since manufacturing drawings may use either convention depending on the origin of the design specification.
What are standard pressure angles and how do they affect gear performance?
Standard pressure angles in modern gear design are 14.5 degrees, 20 degrees, and 25 degrees, with 20 degrees being the most commonly used worldwide. The pressure angle defines the shape of the involute tooth profile and affects several performance characteristics. A larger pressure angle produces a wider, stronger tooth base that resists bending fatigue better, but generates higher radial bearing loads and increases noise. A smaller pressure angle creates a narrower tooth with smoother rolling contact and lower noise, but reduced bending strength. The 20-degree standard offers an optimal compromise between strength and smooth operation for most applications. Both meshing gears must use the same pressure angle, and mixing different pressure angles will cause interference and rapid tooth failure.
How does face width affect gear strength and performance?
Face width is the axial length of the gear tooth and directly influences both bending and surface contact strength. The Lewis equation for bending stress shows that tooth bending strength increases linearly with face width, while the Hertzian contact stress formula shows surface durability also improves with wider faces. However, excessively wide gears are problematic because shaft deflection and manufacturing misalignment cause uneven load distribution across the face, concentrating stress at one end of the tooth. A common design guideline limits face width to 8 to 12 times the module for spur gears. The AGMA face width factor accounts for this effect in strength calculations. Optimal face width balances strength requirements against weight, cost, and load distribution considerations.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy