Calculate gear profile shift coefficient, outside diameter, teeth count, or module from the other values for a full-depth involute gear.
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Gear Profile Shift Coefficient Formula
The gear profile shift coefficient calculator uses the outside diameter formula for a standard full-depth involute spur gear with addendum coefficient ha* = 1.0.
Rearranged forms used by the calculator:
- x = gear profile shift coefficient, dimensionless
- da = outside diameter, also called tip diameter
- m = module, in the same length unit as the diameter after conversion
- z = number of teeth
The calculator lets you enter any three values and solve for the missing one. Length values are converted internally to millimeters before the formula is applied, then converted back to the selected output unit if needed.
- Solving for x: use this when you know the gear outside diameter, module, and number of teeth and want the profile shift coefficient.
- Solving for da: use this when you know the profile shift coefficient, tooth count, and module and want the outside diameter.
- Solving for z: use this to estimate the tooth count from the outside diameter, module, and shift coefficient. The result should normally be a whole number.
- Solving for m: use this when the outside diameter, tooth count, and shift coefficient are known and you need the module.
Common Profile Shift Coefficient Ranges
Profile shift coefficients are dimensionless. The acceptable value depends on tooth count, pressure angle, cutter, backlash, and mating gear geometry.
| Profile shift coefficient x | Typical meaning | Effect on outside diameter |
|---|---|---|
| 0 | Standard gear with no profile shift | da = m(z + 2) |
| Positive, such as +0.1 to +0.5 | Tooth profile shifted outward | Increases outside diameter |
| Negative, such as -0.1 to -0.5 | Tooth profile shifted inward | Decreases outside diameter |
Module and Outside Diameter Unit Reference
| Unit | Millimeter conversion | Use in the formula |
|---|---|---|
| mm | 1 mm | Base unit |
| cm | 10 mm | Converted before calculation |
| m | 1000 mm | Converted before calculation |
| in | 25.4 mm | Converted before calculation |
| ft | 304.8 mm | Converted before calculation |
Example Calculations
Example 1: Calculate profile shift coefficient
You have a gear with an outside diameter of 66 mm, 30 teeth, and a module of 2 mm.
The gear profile shift coefficient is 0.5.
Example 2: Calculate outside diameter
You have a gear with 24 teeth, a module of 3 mm, and a profile shift coefficient of 0.25.
The outside diameter is 79.5 mm.
FAQ
What does a positive profile shift coefficient mean?
A positive profile shift coefficient means the tooth profile is shifted outward from the standard position. In this calculator’s formula, a positive x increases the outside diameter because the term 2x is added inside the diameter equation.
What does x = 0 mean for a gear?
x = 0 means there is no profile shift. For a standard full-depth gear, the outside diameter becomes da = m(z + 2). For example, a 20-tooth gear with module 2 mm and no shift has an outside diameter of 44 mm.
Why is the calculated number of teeth not a whole number?
The number of teeth should normally be an integer. If the calculator gives a decimal value for z, the entered outside diameter, module, or shift coefficient does not match a valid whole-tooth gear under the standard assumptions used by the formula. Check that the units are correct and that the diameter is the outside diameter, not the pitch diameter.