Enter the outside (tip) diameter, number of teeth, and module into the calculator to determine the gear profile shift coefficient.

Gear Profile Shift Coefficient Calculator

Enter any 3 values to calculate the missing variable (assumes a standard full-depth involute gear with addendum coefficient ha* = 1.0).

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Gear Profile Shift Coefficient Formula

The following formulas are commonly used (for a standard full-depth involute gear with addendum coefficient ha* = 1.0) to relate the outside (tip) diameter, number of teeth, module, and the profile shift coefficient. 

d_a = m\,(z + 2 + 2x)\quad\Longrightarrow\quad x = \frac{(d_a/m) - z - 2}{2}

Variables:

  • x is the gear profile shift coefficient (dimensionless)
  • da is the outside (tip) diameter
  • z is the number of teeth
  • m is the module

To calculate the gear profile shift coefficient, divide the outside diameter by the module, subtract the number of teeth and 2, then divide the result by 2.

What is a Gear Profile Shift Coefficient?

The gear profile shift coefficient (also called the addendum modification coefficient) is a dimensionless parameter used in involute gear design that represents how far the generating rack cutter is shifted radially, normalized by the module: x = Δ/m. Profile shift is used to avoid undercut on small-tooth-count gears, increase tooth thickness at the reference circle, tune root/tooth strength, and (in gear pairs) help achieve a desired operating center distance when the sum of profile shifts is selected appropriately.

Profile shift does not change the reference (pitch) diameter d = mz. However, for standard proportions (such as ha* = 1.0), the outside (tip) diameter da increases with positive x and decreases with negative x.

How to Calculate Gear Profile Shift Coefficient?

The following steps outline how to calculate the Gear Profile Shift Coefficient.

  1. First, determine the outside (tip) diameter (da).
  2. Next, determine the number of teeth (z).
  3. Next, determine the module (m).
  4. Finally, calculate the gear profile shift coefficient using the formula x = ((da/m) – z – 2) / 2.
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Outside (tip) diameter (da) = 106 mm

Number of teeth (z) = 50

Module (m) = 2 mm