How this calculator works
Convert the pressure angle to radians before subtracting it from its tangent. The result describes the involute angular function used in gear geometry. This page evaluates that scalar function; it does not generate a tooth profile or determine a gear safety factor.
Formula
inv(α) = tan(α) - α, with α expressed in radians. This pressure-angle tool uses 0 ≤ α < π/2.
Worked example
At 45 degrees, α = π/4 and tan(α) = 1, giving inv(α) = 1 - π/4 ≈ 0.2146018366. At 20 degrees the value is about 0.01490438.
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Frequently asked questions
Why not subtract 20 from tan(20 degrees)?
The angle term must be in radians. The unit selector converts degrees before the subtraction.
Is the answer an inverse tangent?
No. The notation inv refers to the involute function. Arctangent is a different function.
What happens near 90 degrees?
The tangent grows without bound. Exactly 90 degrees is excluded, and values very close to it become highly sensitive to angle changes.