Let’s start with the definition of a trap arm. The Florida Building Code defines it as “that portion of a fixture drain between the trap weir and the vent fitting.” Next, you need to know the definition of a trap weir: it is the top level that water settles to in the U-shaped trap under a sink when there is nothing flowing through it. And the “vent fitting” is the connection to the vertical pipe through the roof that allows air into the drain system, which is necessary for free-flowing drains.
The minimum slope of a trap arm is easy to understand and remember. It is a 1/4” drop per running foot for pipes with a diameter of less than 3”, and 1/8” per foot for pipes larger than 3” diameter.
The maximum slope of a trap arm is based on length of the arm and diameter of the pipe. The maximum slope shrinks as the trap arm gets longer and, conversely, increases as the length of the arm shortens. It also grows and shrinks in tandem the with diameter of the pipe.