Involute Function Calculator

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inv(α) = tan α − α and complete involute gear geometry

Mode

Inputs

Pressure Angle α (°)

Common angles:

Involute Function Results

inv(α) = tan α − α

0.0149

Pressure Angle (rad)

0.3491

cos α

0.9397

sin α

0.3420

tan α

0.3640

inv(20°) = tan(20°) − 0.3491 rad = 0.0149

About the Involute Function

inv(α) = tan α − α is the involute of a circle — the curve traced by unwinding a string from a cylinder. It is the mathematical foundation of modern involute gear tooth profiles.

Why involute gears? The tooth flanks of involute gears maintain a constant velocity ratio regardless of small centre-distance errors, making them the universal standard in power transmission (AGMA, ISO 6336).

Standard pressure angles: 20° is by far the most common; 14.5° appears in legacy systems; 25° is used for high-load applications requiring stronger teeth.

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What is Involute Function Calculator?

Involute Function Calculator computes the involute function used in mechanical engineering to design accurate gear tooth profiles for smooth and efficient power transmission.