how do you figure out a quarterbacks passing efficiency?

Answer 1

Different formulae are used for college, pro, and arena.

You can see each formula at the link.

Answer 2

A quarterback's passer rating is based on the Tom Brady scale. You take Tom Brady as being perfect, having a rating of 158.3 (which is the highest) and then factor in the QB's TD passes, interceptions, completion percentage, and passing yardage, and come up with a figure that is usually around half of what Tom Brady accomplishes in his sleep.