Pipe Slope Calculator — Drain Fall

A drain that is too flat silts up, and one laid backwards floods the room it was meant to empty. The fall is decided before the first length of pipe goes in. Give this calculator any two of the run length, the fall and the slope, and it works out the third. The slope comes back in every form a plan or a plumber might use: percent, 1 in N, inches per foot, millimetres per metre and degrees.

Add the pipe diameter and two more answers appear. One says whether the slope meets the minimum in the International Plumbing Code for that size. The other estimates how fast the water moves when the pipe runs full, so you can see whether it will carry solids away.

Worked Example: 30 Feet of 3-Inch Pipe at a Quarter Inch per Foot

The calculator opens solving for the fall on a 30 ft run of 3 in PVC laid at 0.25 in per ft. It reports:

• Fall: 7.5 in from one end of the run to the other
• Slope: 2.083%, 1 : 48, 20.83 mm per m or 1.193°
• Code check: passes, since a 3 in pipe needs at least ⅛ in per ft (1.04%)
• Running full: about 3.38 ft/s and 74.42 gallons a minute

Load Sample moves on to 12 m of 110 mm pipe falling 150 mm (1 : 80), a 1 : 40 fall that needs a 12 m run to lose 300 mm, and 50 ft of 4 in cast iron falling only 4 in. That last one comes out at 0.08 in per ft and fails the code check.

How the Math Links Fall, Run and Slope

Slope is fall divided by run, with both in the same unit. The other two answers are the same equation turned around. Switch Solve for and the current answer is written into its box, so nothing has to be retyped. Changing the slope format re-expresses the same slope rather than reading your number in the new format, and switching between metric and imperial converts every value. A 1 : N slope needs N above 1, or the tool says: “A 1 : N slope needs N greater than 1. For a quarter inch per foot, N is 48.”

The flow estimate uses Manning’s equation for a full pipe, V = (1/n) × R^⅔ × S^½. Here R is a quarter of the diameter and n is the pipe’s roughness: 0.010 for plastic and 0.013 for cast iron, clay or concrete.

Limits of the Code Check and the Flow Figure

The minimum slopes come from IPC table 704.1: ¼ in per ft up to 2½ in, ⅛ in per ft from 3 to 6 in, and 1/16 in per ft from 8 in. Other codes differ. In the UK, Approved Document H allows 1 : 80 for a 100 mm drain serving a WC, so check the one that applies to you. A drain is designed to run partly full, so the full-pipe velocity is a ceiling, not the speed it will run at. When even that ceiling is under the usual 2 ft/s (0.6 m/s) self-cleansing speed, the tool warns you to add fall.