If the tenon is taking a tension load - its thickness, length, and peg / wedge requirements need to be calculated based on species and forces applied to the tenon.
If a standard tenon passes the engineering requirements but you want to make a through tenon - I use the following:
5X material - 1 1/2" thick tenon
7x material - 2" thick tenon
10x material - 3" thick tenon
Length beyond:
Minimum 1/3 (+/-) of the height of the beam the tenon is passing through.
Note - these guidelines do not replace a thorough engineering review...!