Gear pressure angle (sometimes referred to as angle of obliquity) relates to the angle between a spur gear’s tooth face and the tangent to the pitch circle at the point where force is transmitted. By understanding gear pressure angle calculations and applying the correct formulas, engineers can ensure gears perform efficiently in mechanical systems.

The pressure angle measurement allows engineers to understand load capacity, force transmission and the overall efficiency of a pair of meshed gears. The pressure angle also affects the rate of gear wear and how much noise is produced.  

Common Gear Pressure Angles

There are three typical target pressure angles for gear meshing, each with its own usage and benefits. They include: 

• Pressure Angle = 14.5° - these pressure angles are typically found in older gears, and provide lower strength than more modern gear pressure angles
• Pressure Angle = 20° - recognized by AGMA as best-suited for most applications, offers a good balance of strength and efficiency
• Pressure Angle = 25° - these pressure angles indicate a higher strength gear typically used in heavy-duty applications

Formula for Calculating Gear Pressure Angle

In order to find the pressure angle, a few other measurements are required:

1. Pitch Circle Diameter: the diameter of the imaginary circle at which the gear teeth are fully engaged
2. Base Circle Diameter: the diameter of the imaginary circle defining the involute curve that forms the gear’s tooth profile

The Basic Formula

Pressure angle = cos^-1 (D_b  / D_p)

Where: 

• Base Circle Diameter: (D_b)
• Pitch Circle Diameter: (D_p)

Pressure Angle Calculation Example

For a gear with the following measurements:

• Pitch Circle Diameter (D_p) = 50 mm
• Base Circle Diameter (D_b​) = 47 mm

Using the formula above:

1. Equation: Pressure angle = cos^-1 (D_b  / D_p)
2. Calculation: Pressure angle = cos^-1 (47 / 50)
3. Result: Pressure angle = 19.94

In this case, the pressure angle is approximately 20°, which aligns with AGMA’s standard gear design.

Get Guidance on Gear Pressure Angles & Gear Design

Our expert gear engineers are available to offer guidance on gear design, including finding the appropriate pressure angle for your gear system’s specific application. With calculation guidance and custom gear engineering capabilities, our team is ready to help you get the most out of your gear systems. 

Contact our team of engineers today for more information on gear design and calculations.