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Pressure Angle to Involute Function Value
Evaluate tan(α) − α with the angle converted to radians, for angles from zero up to but excluding a right angle.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
At 45°, α = π/4 radians and tan α = 1, so the involute value is 1 − π/4 ≈ 0.2146018366.
inv(α) = tan(α) − α, with α in radians
Worked example
Enter these known values and leave the other values blank.
- Pressure angle
- 0.7853981633974483096156608458198757210492923498437764552437361481 rad
- Involute function value
- 0.2146
Assumptions and limitations
- The supported angle is at least zero and strictly less than 90° or π/2 radians. The value grows without bound toward that upper endpoint.
- The angle is converted to radians before subtraction even when you choose degrees for entry. The output is dimensionless; it is not an angle in the selected input unit.
- This forward calculation does not solve the inverse involute equation or determine a complete gear profile.
Common questions
Why can I not subtract an angle entered in degrees directly?
The formula requires the radian numerical value. At 45°, subtract π/4 from one, not 45.
Does the output selector follow the input angle unit?
There is no output angle conversion. Changing the input between degrees and radians represents the same angle and preserves the involute value.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.