Ask for a two-inch pipe and you will get a pipe whose outside diameter is not two inches. That is the first thing to understand about pipe sizing, and the schedule system follows from it.
Nominal size and outside diameter
Pipe is sold by nominal pipe size: NPS in the American system, DN in the metric one. The nominal size is a label, not a measurement. For each label the standards fix one outside diameter, and that outside diameter never changes: every NPS 2 pipe, whatever its wall thickness, has the same outside diameter, so the same fittings, clamps and threads fit it. In the smaller sizes the label sits somewhere between the inside and outside diameters for historical reasons; from NPS 14 upward the label and the outside diameter in inches are the same number.
Schedule and wall thickness
If the outside diameter is fixed, the only way to make a pipe stronger is to make the wall thicker, and the schedule is the label for that. Schedule 5, 10, 40, 80, 160: a higher number means a thicker wall for the same nominal size, so a smaller bore and a heavier pipe. The number began as a rough ratio of working pressure to allowable stress, which is why it climbs with pressure duty, but today it is simply the name of a row in a table.
The two facts to hold onto: outside diameter follows the nominal size, and wall thickness follows the schedule. The inside diameter is what is left, the outside diameter less twice the wall.
Why a schedule is a lookup, not a formula
There is no equation that gives the wall for a given schedule. The values were set by committee, size by size, and they are not proportional: schedule 40 wall grows with pipe size, but not in a straight line, and at some sizes schedule 40 and “standard” coincide while at the largest sizes they part. Stainless pipe adds its own series, 5S, 10S, 40S and 80S, whose walls match the carbon-steel schedules at some sizes and differ at others. A calculator that derived wall from schedule by formula would be wrong somewhere, and a pipe that is wrong somewhere is the one that fails. So this site treats schedules the way the standards do: as a table to be read, one of the fixed rules our calculators are built under.
That table is not on the site yet. The schedule lookup, nominal size to outside diameter and wall for each schedule, is being entered and checked row by row against the standards we hold, and it will appear as a tool when it is complete. Until then, the pipe weight calculator takes the outside diameter and wall you read from your own table and gives the theoretical weight per metre from those.
Reading a pipe designation
A line on a drawing that says NPS 4 Sch 40S 316L tells you four things: the nominal size, which fixes the outside diameter; the schedule, which fixes the wall; the S, which means the stainless-steel schedule series; and the grade. What it does not tell you is the weight, the inside diameter or the pressure rating. Those follow from the first two through the table, the grade, the temperature and the design code, and the design code is not something a website should stand in for.