Online Calculator

Inverse Involute

For many calculations – e.g. to determine the dimension over two balls from the tooth thickness – it is necessary to transform involute alpha to the pressure angle.

The required function is non-reversible. Therefore, the pressure angle can only be calculated approximately. That is what this tool does.

Type in the value for the involute angle (in radians) and the corresponding pressure angle will be calculated.


Involute Alpha (rad):


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Diametrical Size at Reversal Point

There are different instruments to inspect the size over/between two balls. The most simple instrument is based on the rocking method. These hand-held instruments are equipped with measuring inserts and a dial indicator. The nominal size is adjusted by gauge blocks. Afterwards, the operator needs to find the reversal point to receive the relative deviation.

Special case helical gears with odd number of teeth

The reversal point will not coincide with the required measuring plane (perpendicular to the gear axis). As a consequence, the operator detects a higher deviation.

To use the available measuring instrument anyway, it must not be adjusted to the nominal size but to the dimension at the reversal point. This can be calculated online with following tool.
Type in your gear data below.

Gearing type:

Number of teeth:

Module in mm:

Helix angle in degree:

Nominal MdK over/between balls in mm:

Ball diameter in mm: