Gallons Per Foot of Pipe by Inside Diameter

Why this matters

How much water is in a run of pipe sets a surprising number of field decisions: how much antifreeze a hydronic loop needs, how long a customer waits for hot water at a far fixture, how many gallons drain out when you cut a line, how long a flush has to run to turn the pipe's contents over, how much a chemical treatment has to be. Get the volume wrong and the antifreeze is too weak to protect the loop, or the flush stops before the old water is out.

There is one formula behind all of it, and it is short. The part that trips people is the input: the formula wants the inside diameter, and the size printed on the pipe is not that. A 3/4 in copper line and a 3/4 in plastic line do not hold the same water per foot. This card derives the number, gives a starting table, and shows how much the real bore moves the answer.

The formula and where 0.0408 comes from

Gallons per foot = 0.0408 x (inside diameter in inches) x (inside diameter in inches).

Derivation, with units carried:

1. The cross-section of the bore is a circle: area = 0.7854 x ID x ID, in square inches.
2. One foot of pipe is 12 in long, so the volume of one foot is 0.7854 x ID x ID x 12 in = 9.4248 x ID x ID, in cubic inches per foot.
3. One gallon is 231 cubic inches, so divide: 9.4248 / 231 = 0.0408.

So 0.0408 x ID squared gives gallons per foot when ID is in inches. Nothing about the pipe material is in the constant; it is pure geometry. Everything material-specific lives in the ID. See related: Circles in the Field: Area, Circumference and the Diameter Trap for the 0.7854, and The Water Constants 7.48, 8.34 and 231 for the 231.

The squared term is what makes the ID matter. A small error in the diameter becomes roughly twice that error in the volume. An ID that is 5 percent larger than you assumed holds about 10 percent more water.

The starting table: if the bore were the nominal size

This table uses the formula with the nominal size as the ID. It is a starting point for a rough estimate, not the answer for any particular pipe.

GALLONS PER FOOT, BORE TAKEN AS NOMINAL SIZE
   gal/ft = 0.0408 x ID x ID   (ID in inches)
-----------------------------------------------
 ID (in)   ID x ID    gal per ft   ft per gal
 -------   -------    ----------   ----------
  0.50      0.250       0.010         98
  0.75      0.563       0.023         44
  1.00      1.000       0.041         25
  2.00      4.000       0.163          6.1
  4.00     16.000       0.653          1.5
-----------------------------------------------
 note: real ID differs by material and wall

Two patterns in it are worth carrying in your head:

• About 25 feet of 1 in pipe holds a gallon. That one anchor is a good rough check for anything in the small-pipe range.
• Doubling the diameter quadruples the volume. 2 in holds four times what 1 in holds per foot, and 4 in holds four times 2 in. A 4 in line holds sixteen times a 1 in line.

Why nominal size is not the inside diameter

Pipe and tube sizes are names. Depending on the product, the name is tied to the outside diameter, to an old inside dimension, or to nothing measurable at all, and the wall thickness then sets the bore.

• Copper tube in plumbing sizes has an outside diameter that is 1/8 in larger than its nominal size (3/4 in copper is 0.875 in OD), and the wall thickness depends on the type. Type K has the thickest wall, Type L is in the middle, Type M is the thinnest. So three 3/4 in copper tubes have three different bores.
• Steel pipe and plastic pipe in iron-pipe sizes (Schedule 40, Schedule 80) share an outside diameter for a given nominal size, and the schedule sets the wall. Schedule 80 has a thicker wall and a smaller bore than Schedule 40 of the same size.
• PEX and other tubing sized to copper outside diameters commonly have a thick wall relative to their size, so their bore is noticeably smaller than the nominal number suggests.

The only reliable ID is the one published by the pipe's manufacturer or the standard it is made to, for that exact type or schedule. Some published values for common products, worked through the formula:

Compare each row against the nominal table. The Type L copper rows run about 5 to 19 percent above the nominal figure (5 at 1 in, 9 at 3/4 in, 19 at 1/2 in), because the copper bore is larger than its name and the gap matters most on the smallest sizes. The Schedule 40 2 in row runs about 7 percent above. The 1/2 in Schedule 40 steel is the biggest jump in the group: 0.0158 against 0.010, more than half again.

For tubing with a thick wall, the effect runs the other way. Thick-walled tubing sized to a 1/2 in copper outside diameter can have a bore below 0.5 in, which puts it under the nominal table rather than over it. Look up the ID for the exact product and its dimension ratio rather than assuming one.

When you do not know what the pipe is

On an existing system the markings are often painted over or gone. Three field moves narrow it down:

• Measure the outside. Wrap a tape around the pipe and divide by 3.1416, or read it with calipers. An OD of 0.875 in on metal tube says 3/4 in copper; an OD of about 2.375 in says 2 in iron-pipe size, steel or plastic. The OD tells you the family and the size, not the wall.
• Look at a cut end or an open fitting. If any end is exposed (a cap off, a section removed for the repair), measure the wall or the bore directly. That reading beats any table.
• Read the print on another length. Plastic pipe and tubing are usually printed every few feet with the size, schedule or dimension ratio, and the standard. One legible length elsewhere on the system often identifies the whole run.

The wall matters more than people expect. 2 in Schedule 80 has a published ID of 1.939 in, so 0.0408 x 1.939 x 1.939 = 0.1534 gal/ft, about 12 percent less than the 0.1743 of Schedule 40 at the same outside diameter. Write down which assumption you made if you could not confirm it.

The worked example: antifreeze for a hydronic loop

A tech is filling a small hydronic loop with an antifreeze solution and needs the loop volume to mix it. The piping is 120 ft of 3/4 in Type L copper (supply and return together), plus a boiler and a set of baseboard emitters whose water content comes from their own literature.

Step 1, the pipe, using the real ID. ID = 0.785 in. gal/ft = 0.0408 x 0.785 x 0.785 = 0.0408 x 0.6162 = 0.0251 gal/ft. Pipe volume = 120 ft x 0.0251 gal/ft = 3.02 gal.

Step 2, what nominal would have said. 120 ft x 0.023 gal/ft = 2.76 gal. The nominal estimate is 0.26 gal short, about 9 percent under the real pipe volume.

Step 3, add the rest of the loop. The boiler's heat exchanger and the emitters hold water too, and on a small loop they can hold more than the piping. Their volumes come from the manufacturer's literature for those exact units, and they get their own lines. See related: How to Figure the Fill Volume of a Piping Loop, which owns the whole-loop total.

Step 4, why the 9 percent matters. The antifreeze is dosed as a percentage of the total. If the system holds more water than the calculation assumed, the same volume of concentrate makes a weaker solution, and the freeze protection printed on the concentrate's chart no longer applies. The error runs in the unsafe direction: an underestimated volume always dilutes the mix. That is the case for using the published ID and, in the end, for checking the mixed solution with a refractometer or test strip rather than trusting the calculation alone.

Rough check. 120 ft of roughly 3/4 in pipe at about 44 ft per gallon is just under 3 gallons. The real 3.02 gal sits right there. If the answer had come out near 30 gallons or 0.3 gallons, a decimal moved.

The same number, other jobs

Hot-water wait. The water sitting in the line between the heater and a fixture has to run out before hot water arrives. 60 ft of 3/4 in Type L copper holds 60 x 0.0251 = 1.51 gal. At a fixture flowing 1.5 gal per minute, that is about a minute of waiting, ignoring the heat the pipe itself soaks up (which makes the real wait longer). See related: How to Work Out a Fill or Drain Time.

Draining a section. Before cutting into a 2 in Schedule 40 line, 40 ft of pipe above the cut holds 40 x 0.1743 = 6.97 gal. That is more than a 5-gallon bucket. Plan the container before the cut, not after.

Flushing. A flush that has to replace the contents of a line some number of times needs the line volume first. Multiply the gal/ft by the length, then by the number of turnovers the procedure calls for.

Chemical treatment. Any treatment dosed per gallon of system water needs the volume, and a dose built on the nominal figure for a thick-walled tubing system overdoses, while one built on nominal for copper underdoses. Same formula, opposite error.

What this table does not cover

• Fittings, valves and equipment. Elbows and tees add a little; boilers, heat exchangers, tanks and emitters can add a lot. Get those from the equipment literature.
• Partly full pipe. A drain line runs partly full. Its volume depends on the depth of flow and is not this calculation.
• Liquids other than water. The volume in gallons is the same for any liquid; the weight is not. Use the gallons from this card and the density from the fluid's data sheet. See related: The Water Constants 7.48, 8.34 and 231.

References

• Pipe and tube manufacturer dimension tables, and the product standard the pipe is made to, for published inside diameters by type and schedule
• See related: Circles in the Field: Area, Circumference and the Diameter Trap
• See related: The Water Constants 7.48, 8.34 and 231
• See related: How to Figure the Fill Volume of a Piping Loop
• See related: How to Work Out a Fill or Drain Time