Diameter vs height

I have a gearbox which steel pins are inserted into. The pins are used as "axles" for the gears and I would like to know the recommended ratio of a pin height to diameter and still maintain stability. The pins are .098 in dia with a hardness of 60 rc. The tops of the pins are supported by a hole in the gearbox cover. Thanks for any help in advance.

Normally we find out the axle dia before designing using calculations. Here in your case you already have the axle dia. then you your are looking for ration..Height of axle depends on the mounting position of your shaft.