Pipe Volume Calculator

How to Calculate Pipe Volume

A pipe holds a cylinder of water: the area of the bore times the length. The only hard part is the diameter. The nominal size printed on the pipe is a name, not a measurement, and the inside diameter of a 3/4 inch pipe changes with the material and wall thickness.

Plumbers need pipe volume for hot water wait times, for filling and treating hydronic systems with glycol, for sizing expansion tanks, for flushing and disinfecting new lines, and for estimating the weight of full pipe on hangers.

Nominal Size vs. Inside Diameter

Copper water tube (ASTM B88) and PEX (ASTM F876) use copper tube size: the outside diameter is always 1/8 inch larger than the nominal size. Type K, L and M copper share the same outside diameter and differ only in wall thickness, so Type M has the largest bore. PEX has a much thicker wall, so its bore is smaller than copper of the same nominal size.

PVC (ASTM D1785) uses iron pipe size, with a larger outside diameter than copper. Schedule 80 has a thicker wall and smaller bore than Schedule 40.

• 3/4 inch Type K copper: 0.745 in inside diameter.
• 3/4 inch Type L copper: 0.785 in.
• 3/4 inch Type M copper: 0.811 in.
• 3/4 inch PEX: 0.681 in.
• 3/4 inch PVC Schedule 40: 0.824 in. Schedule 80: 0.742 in.

Pipe Volume, Velocity and Friction Formulas

With d as the inside diameter in inches, a gallon is 231 cubic inches, so each foot of pipe holds 12 × π/4 × d² ÷ 231 gallons. Velocity follows from the same area. Friction loss uses the Hazen-Williams equation for water at ordinary temperatures.

d

Inside diameter in inches

L

Length of pipe in feet

V

Velocity in feet per second

C

Hazen-Williams roughness coefficient (higher is smoother)

R

Hydraulic radius in feet, d ÷ 48 for a full round pipe

S

Friction loss in feet of head per foot of pipe

Copper and PEX inside diameters use the nominal wall; PVC uses the minimum wall in ASTM D1785. Real pipe varies slightly within the standard’s tolerances, so published volumes can differ by a few percent.

Worked Example: Hot Water Wait Time

A bathroom sink is fed by 25 ft of 3/4 inch Type M copper and 30 ft of 1/2 inch Type M copper from the water heater. The faucet runs at 2 GPM.

1. 3/4 inch Type M: 0.811 in ID, 0.0268 gal/ft × 25 ft = 0.671 gal.
2. 1/2 inch Type M: 0.569 in ID, 0.0132 gal/ft × 30 ft = 0.396 gal.
3. Total in the pipe: 1.067 gal. At 2 GPM, that is 32 seconds just to push the cold water out.

Result: at least 32 seconds and over a gallon wasted per use. In practice it is longer, because the first hot water cools on the cold pipe walls.

Worked Example: Velocity in a 6 GPM Cold Branch

A 6 GPM cold water branch in Type L copper, C = 140, with the CDA cold water limit of 8 ft/s.

1. 1/2 inch (0.545 in ID): 0.4085 × 6 ÷ 0.545² = 8.3 ft/s, over the limit, and 25.5 psi of friction per 100 ft.
2. 3/4 inch (0.785 in ID): 4.0 ft/s and 4.31 psi per 100 ft.
3. 1 inch (1.025 in ID): 2.3 ft/s and 1.18 psi per 100 ft.

Result: of these three common sizes, 3/4 inch is the smallest under the limit. The friction drop from 1/2 to 3/4 inch, about six times, matters more than the velocity on a long run.

Worked Example: Glycol for a Hydronic System

A small hydronic loop has 150 ft of 3/4 inch PEX and 40 ft of 1 inch Type L copper. The boiler lists 2 gallons of water content. The installer wants a 40% propylene glycol mix.

1. PEX: 0.681 in ID, 150 ft holds 2.84 gal.
2. Copper: 1.025 in ID, 40 ft holds 1.71 gal.
3. System: 2.84 + 1.71 + 2 = 6.55 gal.
4. Glycol at 40%: 6.55 × 0.40 = 2.62 gal of concentrate.

Result: about 2.6 gallons of glycol, plus whatever the emitters, buffer tank and air separator hold from their spec sheets.

Gallons per 100 Feet of Pipe

Water held by 100 feet of each pipe type and size, calculated from the inside diameter. A dash means the size is not made in that type.

Maximum GPM in Type L Copper by Velocity Limit

The Copper Development Association recommends 5 to 8 ft/s for cold water, 4 to 5 ft/s for hot water under 140°F, and 2 to 3 ft/s above 140°F. This table uses the top of each range.

Field Tips

Practical advice from plumbers on the HeatingHelp forum and from Green Building Advisor, Contractor magazine and the Copper Development Association.

1. 1

   Expect to waste about twice the pipe volume

   Hot water researcher Gary Klein’s rule of thumb is that it takes about twice the pipe’s volume to get hot water at the tap, and measurements in 3/4 inch pipe found 1.5 to 2.5 times. Shorter, smaller hot lines or a recirculation loop are the fix.

2. 2

   Slow down recirculation loops

   An oversized recirculation pump is a common cause of pinhole leaks in copper. One HeatingHelp case pumped 10 GPM through 3/4 inch Type L, about 6.6 ft/s, far above the 2 to 3 ft/s usually recommended for hot water loops. A smaller pump and flow control ended the leaks.

3. 3

   Ream every cut

   The burr left by a tubing cutter makes turbulence right at the joint, which strips copper’s protective film and starts erosion. Ream copper to full bore before soldering or pressing, and use long-radius fittings where the pipe changes direction often.

4. 4

   PEX runs faster than copper of the same size

   1/2 inch PEX has a 0.485 in bore against 0.545 in for Type L copper, so it has about 21% less area. At 4 GPM, the PEX runs at 6.9 ft/s against 5.5 ft/s in copper, with more friction loss. Size up a step on long PEX runs.

5. 5

   Count everything before adding glycol

   Pipe is only part of a hydronic system’s volume. Add the boiler, emitters, buffer tank and air separator from their spec sheets, then mix to the glycol maker’s freeze chart. The same total system volume sizes the expansion tank.

Sources: Green Building Advisor: Why your hot water takes so long, Contractor: Ruined by recirc, HeatingHelp: Velocity, Caleffi: Copper velocity limits from the Copper Development Association, R.L. Deppmann: Expansion and compression tanks