Pipe Volume Calculator

Background.

Fifty feet of 3/4 inch Type L copper between a water heater and a kitchen tap holds about 1.26 gallons. Every drop of that has to run out of the faucet, already cooled, before hot water arrives: roughly 34 seconds at 2.2 gallons a minute, and longer in practice because the cold pipe takes heat from the first hot water that reaches it. Questions like this one, and bigger ones about dosing, flushing and filling pipework, all start from the same number, the volume of liquid a run of pipe holds.

That number cannot be read off the size stamped on the pipe. Pipe and tube are sold by trade size, a label that fixes the outside diameter within a family of products, while the wall thickness, and so the bore, depends on the material and its schedule or type. Three-quarter inch Schedule 40 steel has a bore of 0.824 inch; 3/4 inch PEX built to SDR-9 has a nominal bore of about 0.6806 inch, so a foot of the steel holds about 47 percent more water. Choose the material and size here and the dimensions come from the published standards: ASME B36.10M for steel pipe, ASTM D1785 for PVC and CPVC, which share steel's outside diameters and schedule walls, ASTM B88 for copper water tube Types K, L and M, and ASTM F876 for PEX.

Tradespeople reach for the figure in several situations. Disinfecting a new or repaired water main means mixing chlorine to a concentration, which is impossible without knowing the volume being treated. Flushing is often specified in pipe volumes rather than minutes. A closed heating loop needs a known quantity of glycol, and the system volume is one of the inputs to sizing its expansion tank. Draining a system before winter, or working out how many gallons will spill when a line is cut, is the same calculation. So is the load on hangers, because a long suspended run full of water is heavier than it looks.

The result is the capacity of a completely full, straight run of one pipe size. It leaves out fittings, valves and any tanks, heaters or radiators connected to the pipe, and it does not size anything: pipe sizing and disinfection procedures are set by the plumbing code and health authority where the work is done.

What is pipe volume calculator?

Pipe volume is the internal capacity of a length of pipe, the amount of liquid it holds when completely full. It equals the cross-sectional area of the bore multiplied by the developed length of the run, and it is usually given in US gallons, litres or cubic feet. The bore is the outside diameter minus twice the wall thickness, and that is where pipe families differ. Steel and plastic iron pipe size (IPS) products keep the same outside diameter at every schedule, so 2 inch pipe always measures 2.375 inches across the outside and a higher schedule number simply adds wall on the inside. Copper water tube uses copper tube size (CTS), where the outside diameter is the nominal size plus 1/8 inch, and Types K, L and M are progressively thinner walls on the same outside diameter. PEX shares the CTS outside diameters but is specified by a standard dimension ratio: SDR-9 means the minimum wall is one ninth of the outside diameter, which leaves a bore of seven ninths of it. Developed length is the length measured along the centreline of the pipe through every bend and offset, not the straight-line distance between its two ends.

How to use this calculator.

1. 01Choose the material and schedule or type. The print line on steel and plastic pipe gives the schedule; US copper tube is colour-coded, with a green stripe or lettering for Type K, blue for Type L and red for Type M.
2. 02Choose the nominal trade size printed on the pipe. The 3, 4 and 6 inch sizes are available for the steel and PVC schedules only, because copper and PEX are tabulated from 1/2 to 2 inches.
3. 03For anything not in the list, such as larger copper, metric tube, lined pipe or PEX from a specific manufacturer, choose Custom and enter the outside diameter and wall thickness in inches from a data sheet or calipers. Divide millimetres by 25.4. A wall of 0 suits hose and tubing that are sold by their bore, such as a 5/8 inch garden hose.
4. 04Enter the developed length of one run in feet, inches or metres, following every rise, drop and offset. Measuring point to point along a wall will usually come out short.
5. 05If several runs share the same pipe and length, such as three 40 foot branches of 3/4 inch Type L, enter one length and set the number of runs to 3 rather than adding them by hand.
6. 06Read the volume in gallons, litres or cubic feet, and keep the gallons per foot if you will need other lengths later. Check the inside diameter shown against your pipe; if it does not match, switch to Custom.

The formula.

V = π × ((OD − 2t) ÷ 2)² × L ÷ 231. OD is the outside diameter and t the wall thickness, both in inches, so OD − 2t is the bore; half of it is the radius, and π times the radius squared is the area of the opening in square inches. L is the developed length in inches, the length of one run times the number of runs, converted from feet (× 12) or metres (× 39.37008, because an inch is exactly 2.54 cm). Area times length gives cubic inches, and dividing by 231 gives US gallons, since a US gallon is defined as exactly 231 cubic inches. Litres follow from the exact relation 1 US gallon = 3.785411784 litres, and cubic feet from 1 cubic foot = 1,728 cubic inches, also exact. Capacity per foot is the area × 12 ÷ 231, and the weight of the water is gallons × 8.34 lb, the figure used for water near 60 °F on US water-operator conversion sheets. The bore enters the equation squared, which makes it the term to get right: a bore 2 percent too large overstates the volume by about 4 percent. For 1/2 inch PEX, the nominal SDR-9 bore of 0.4861 inch against the roughly 0.475 inch that tubing makers publish means real tubing holds about 4.5 percent less than the nominal figure suggests. Length, by contrast, enters linearly, so a 10 percent error in the measured run is a 10 percent error in the answer and no more. The model is a straight cylinder, full to the top, of uniform bore. It knows nothing of fittings, scale or corrosion inside old steel, or the slightly heavier walls that plastic pipe is often extruded with.

A worked example.

Frequently asked questions.

References& sources.

1. [1]ASME B36.10M, Welded and Seamless Wrought Steel Pipe — outside diameters and Schedule 40 / 80 wall thicknesses for NPS 1/2 through 6. The standard is sold by ASME; the dimensional rows used here were read from two independent republishers that both name ANSI/ASME B36.10M and whose inch and millimetre values agree.
2. [2]Engineers Edge — Schedule 40 steel pipe sizes and dimensions, citing ANSI/ASME B36.10M-1995. Source of the Schedule 40 outside diameter, wall thickness and inside diameter rows used in this calculator.
3. [3]Engineers Edge — copper tubing size chart to ASTM B88, giving outside diameter and Type K, L and M wall thickness and inside diameter for nominal 1/2 through 2 inch.
4. [4]ASTM F876, Standard Specification for Crosslinked Polyethylene (PEX) Tubing — the SDR-9 requirement that fixes minimum wall at one ninth of the outside diameter, from which the nominal bore used here is derived. Standard is available for purchase from ASTM International.
5. [5]ASTM D1785, Standard Specification for Poly(Vinyl Chloride) (PVC) Plastic Pipe, Schedules 40, 80 and 120 — the specification that places PVC and CPVC on the same iron pipe size outside diameters and schedule wall thicknesses as steel. Standard is available for purchase from ASTM International.
6. [6]California State Water Resources Control Board, Division of Drinking Water — water treatment operator certification examination conversion sheet (2016), giving the weight of water as 8.34 pounds per US gallon.
7. [7]PipeFlowCalculations — PVC Schedule 40 dimension chart citing ASTM D1785, used as the secondary check on the PVC wall thicknesses. Its 1 inch row prints 1.32 in outside diameter where the IPS series gives 1.315; this calculator uses 1.315.