Compressed air is dense, and that is the whole trick
At 110 psi gauge and 80 degrees, air in a pipe is 8.3 times as dense as the air in the room. A hundred cubic feet of free air a minute occupies about 12 cubic feet a minute once it is in the line, which is why a shop main is an inch across and a dust collector duct is eight. It also means the friction loss depends on the line pressure: run the same flow at 60 psi instead of 110 and the air is half as dense, takes up twice the space, moves twice as fast, and the drop goes up by roughly four times.
Get the barometric field right if you are up high. At 5,000 feet the atmosphere is near 12.2 psia, a free cubic foot is a bigger thing, and everything on the page moves.
What the defaults come out at
100 cfm of free air down 120 feet of 1 inch schedule 40, with six elbows, two turned tees and two ball valves, works out to 147 effective feet, 33 feet per second, a Reynolds number near 149,000 and a friction factor of 0.0245. That is 3.11 psi along the main.
Then the hose. 15 cfm through 25 feet of 3/8 inch bore is 2.79 psi — nearly as much as 147 feet of pipe, from 25 feet of hose, because the bore is a third of the size and the loss runs roughly as the inverse fifth power of the bore. Two couplers at 1.5 psi each and 3 psi through the filter, regulator and lubricator finish the job. 110 psi at the header arrives as 98.1 psi at the tool, and the last four feet of the path account for more of the loss than the first hundred and twenty.
The bore column
The block that lists every size runs the same flow, length and fitting count through each bore, so it is a computed comparison rather than a rule. At the default flow the 1/2 inch line drops 43.76 psi, the 3/4 drops 10.45, the 1 inch drops 3.11, the 1-1/4 drops 0.80, the 1-1/2 drops 0.38 and the 2 inch drops 0.11. Each step up cuts the loss, and the size of the cut shrinks fast — going from 1 to 1-1/4 saves 2.31 psi, going from 1-1/2 to 2 saves 0.27.
Which is the point of printing all of them instead of a recommendation. What the extra bore is worth depends on what the pipe and the labour cost, and on whether the shop is going to grow into it; a main that is generous for today is the cheap version of a main that gets replaced in five years.
The hose is where the pressure actually goes
Almost every complaint about a slow air tool ends at the hose, the couplers or a loaded filter element, and almost every attempted fix starts at the compressor. A 50 foot 1/4 inch hose feeding a tool that wants 15 cfm is a different world from the 3/8 inch default here — same flow, same length doubled and the bore cut by a third, and the drop goes from 2.79 psi to 46.88. That leaves 54 psi at the tool instead of 98. Coupler bodies of the same nominal size differ by a factor of three or four between makes, which is why the page asks for your figure rather than printing one.
The lubricator and the regulator are the other overlooked pair. Their published curves are at a stated flow, and the loss climbs steeply above it. A filter element that reads 3 psi differential when it is new and 12 when it is loaded has quietly taken nine psi off every tool in the shop.
Where this model runs out
It treats the air density as constant along the run, which is the standard simplification and is fair while the drop is small compared with the absolute pressure. At the defaults the main loses 3.11 psi out of 124.7 psia, which is 2.5 percent, and the error from the assumption is well inside the error in the roughness figure. Push the flow up until the drop is a fifth of the absolute pressure and the assumption stops being reasonable; the air expands as it travels, accelerates as it expands, and the real loss runs above what the page prints. The page says so on screen when it happens.
Questions people ask
What size pipe do I need for a shop air line?
That depends on the flow, the length, the pressure you start at and how much pressure you are prepared to lose, which is why this page prints the drop at every bore rather than naming a size. At 100 cfm down 120 feet with a normal fitting count, 3/4 inch loses 10.45 psi, 1 inch loses 3.11 and 1-1/4 loses 0.80. Put your own flow and length in and read the column. Nothing here says a particular loss is acceptable — that is a decision about your tools and your pressure headroom.
Why does my air tool run slow when the compressor gauge reads fine?
Because the gauge is in the compressor room and the tool is not. At the defaults on this page, 110 psi at the header arrives at the tool as 98 psi, and more than half of that loss happens in the last 25 feet of hose, the two couplers and the filter and regulator. Put gauges either side of each piece and the culprit shows up in one afternoon. Turning the regulator up masks it and makes every leak in the building flow harder.
Does hose length matter more than pipe length?
Foot for foot, enormously, because the bore is so much smaller and the loss runs roughly as the inverse fifth power of the bore. In the default run, 25 feet of 3/8 inch hose loses 2.79 psi while 147 effective feet of 1 inch pipe loses 3.11. Coiled hose on a reel counts in full — the air sees the whole length whether it is coiled or not. Going up one hose size usually does more for a struggling tool than anything upstream of the drop.
Should I use the schedule 40 bore or measure the pipe?
Measure it if the system is old. Schedule 40 bores are the right starting point for new black iron, but galvanised pipe that has been in service for decades has lost bore to scale, and lost bore hurts far more than the added roughness does. Aluminium and composite systems have their own bores that are not the schedule 40 figures at all, so use the manufacturer dimension for those. The measured bore mode is there for both cases.
Why does the calculator ask for barometric pressure?
Because free air is measured against the air outside, and the air outside is thinner the higher you are. At 5,000 feet the atmosphere is near 12.2 psia rather than 14.7, so a cubic foot of free air is less air, the density ratio in the pipe changes, and both the flow arithmetic and the pressure drop move with it. Leaving it at 14.7 near sea level is fine; leaving it at 14.7 in Denver is not.