The diameter of the worm wheel does not have anything to the rate that it will multiply the torque, except for the loses in efficiency, but it does have in HOW MUCH TORQUE you can multiply.
That is a 2" 40 teeth worm gear mated to a single thread worm will multiply the torque supplied in the input shaft by a factor of 40, and it will work probably well up to a 2 HP input at 1750 rpm, but if you multiply the torque input of the motor by reducing the input speed, lets say via a pulley/belt arrangement then probably if you try to use the full output torque what you would get is a stripped tooth for the worm wheel. The same applies if you raise the input torque with a bigger motor.