Gravity does the work

There is no pump on the drain side of a building. Every fixture you will ever rough in drains for one reason only: the pipe tilts.

The compromise

More slope is not better. A drain moves two things at once — water and solids — and they only travel together inside a narrow band of pitch:

• Too flat and the water hasn't the velocity to carry anything; it pools, and the solids settle where they stop.
• Too steep — past about ½ in/ft on a horizontal run — and the liquid races ahead, drains away, and leaves the solids stranded in a dry pipe. A "steep horizontal" isn't a faster drain; it's a slower clog. Past that, the run belongs on a 45° or a vertical drop, where everything free-falls together.

The code bands

The minimum slope goes by diameter, because bigger pipes keep carrying velocity at gentler pitch:

The math is one multiplication

Fall = slope × run. A 40 ft run of 4″ pipe at its minimum ⅛ in/ft drops 40 × ⅛ = 5 inches end to end. That's the number you actually use on site: mark it on the level or set it on the laser, and the pitch takes care of itself. The drain slope calculator turns any pipe-and-run combination into that fraction.

Why this matters

Callbacks for "slow drain" are rarely about the fixture — they're about a run that was laid outside the band. Get the pitch right at rough-in, when it costs a string line and ten minutes, not after the slab is poured.