PlumbMath

Methodology

How each calculator on this site computes its results, where every number comes from, and what it leaves out. One section per tool, each with its equations, the code sections and tables read, its limits, its sources and the dates they were checked. The footer date is the earliest of those checks.

Gas pipe sizing

How the gas pipe sizing calculator computes its results, where each number comes from, and what it leaves out. Sources were last checked on October 2, 2026.

Scope

  • Natural gas with a specific gravity of 0.60.
  • Delivery pressure below 1.5 psi, where the low pressure equation applies.
  • Schedule 40 steel pipe, 1/2 in. to 4 in., and semirigid copper tubing of Type K or L, 1/4 in. to 2 in.
  • The longest length method and the branch length method.

Equations

Minimum inside diameter

International Fuel Gas Code (IFGC) 2024, Section 402.4, Equation 4-1, the low pressure gas equation for less than 1.5 psi. The Uniform Plumbing Code (UPC) 2024 prints the same equation in Section 1215.3.

D = Q to the power 0.381 ÷ (19.17 × (ΔH ÷ (Cr × L)) to the power 0.206)

Capacity of a pipe

IFGC 2024 Appendix A, Section A104, low pressure form. Appendix A states that it is informative and is not part of the code.

Q = 2,313 × D to the power 2.623 × (ΔH ÷ (Cr × L)) to the power 0.541

D
Inside diameter of the pipe, inches
Q
Gas flow, cubic feet per hour at 60°F and 30 inch mercury column
ΔH
Pressure drop, inches water column (27.7 inch water column = 1 psi)
L
Equivalent length of pipe, feet
Cr
0.6094 for natural gas, IFGC Table 402.4 (UPC Table 1215.3 prints the same value)

The two forms are the same relation with rounded exponents, so they differ slightly. The capacity form gives the lower capacity of the two and is the one we use for the pass or fail test. In our tests it agrees with a sample of the published low pressure tables of the code for steel pipe and copper tubing within the rounding of the printed values. A size is selected only where both checks pass: its computed capacity is at least the load, and its inside diameter is at least the Equation 4-1 diameter. The minimum inside diameter shown in the result is the larger of the Equation 4-1 diameter and the diameter at which the capacity form equals the load.

The code also prints a high pressure equation (Equation 4-2) for 1.5 psi and above, with absolute pressure taken as gauge pressure plus 14.7. The calculator does not use it. See the limits below.

From appliance input to gas flow

  • Flow in cubic feet per hour = appliance input in Btu per hour ÷ heating value of the gas in Btu per cubic foot (IFGC Appendix A102.1, UPC 1214.3).
  • Take the input from the appliance rating plate. Get the heating value from your gas supplier. The form starts at 1,000 Btu per cubic foot because the IFGC Appendix A examples assume that value. The UPC example in Figure 1215.1.1 assumes 1,100.
  • The load of a section is the sum of all appliances downstream of it, all running at full input at the same time (IFGC 402.2, UPC 1208.3.1). Loads are not rounded before they are added. No diversity factor is applied.
  • The form accepts heating values from 800 to 1,300 Btu per cubic foot. That range is a typing error guard of this tool, not a code value. A notice is shown where the value is still the form default, and where it is above 1,100, because a heating value that is too high makes the computed flow too low.
  • An appliance input below 1,000 Btu per hour is not accepted. Rating plates give Btu per hour, for example 80,000, and a smaller number is almost always a rating typed in thousands of Btu per hour (MBH). That limit is a typing error guard of this tool, not a code value.

Length methods

  • Longest length method (IFGC 402.4.1, UPC 1215.1.1). Every section is sized with the longest length of piping from the point of delivery to the most remote outlet, and the load of the section.
  • Branch length method (IFGC 402.4.2, UPC 1215.1.2). Sections on the longest run are sized with the longest run. Every other section is sized with the length from the point of delivery to the most remote outlet in its branch.
  • Length handling. By default the sizing length is rounded up to the next length row of the code tables (10 ft to 2,000 ft), the way the tables are read. This is never less conservative than the exact length. With the exact length option the length is used as entered, but never less than 10 ft.
  • Sizes the tables do not print. The notes of IFGC Tables 402.4(1), 402.4(2), 402.4(8) and 402.4(9) say that NA means a flow of less than 10 cubic feet per hour. With the table rows option a size whose computed capacity at the sizing length is below 10 cubic feet per hour is not selected, and the next size is taken, the way the table is read. With the exact length option the size from the equation is shown with a notice.

Fittings and valves

The length L in the equations is the equivalent length of pipe (IFGC 402.4). IFGC Appendix A102.2 says an allowance in equivalent length should be considered for any piping run with 4 or more fittings, and A103.1 says the same for piping segments. The appendix does not say what to do with fewer. The calculator adds the allowance for every fitting and valve you enter, whatever their number. That is a choice of this tool on the conservative side. It also means the result does not depend on how you split a run into sections.

The allowance for one fitting is the inside diameter in inches times n ÷ 12, in feet, where n is the length to diameter ratio of the fitting given in the heading of Table A102.2 of the appendix (A103.1). The ratio used for each fitting is shown in the math of every section that has fittings. Because the allowance depends on the pipe size, the calculator repeats the sizing until the sizes stop changing. For copper valves the allowance is taken 45 percent longer (A103.1).

Pipe diameters

Schedule 40 steel pipe
Nominal size (in.) Inside diameter (in.)
1/2 0.622
3/4 0.824
1 1.049
1-1/4 1.380
1-1/2 1.610
2 2.067
2-1/2 2.469
3 3.068
4 4.026

Source: the row "Actual ID" in the header of IFGC Tables 402.4(1) and 402.4(2). Table A105.1 of Appendix A lists the same diameters.

Semirigid copper tubing (Type K or L)
K and L nominal size (in.) Outside diameter (in.) Type K inside diameter (in.)
1/4 3/8 0.305
3/8 1/2 0.402
1/2 5/8 0.527
5/8 3/4 0.652
3/4 7/8 0.745
1 1-1/8 0.995
1-1/4 1-3/8 1.245
1-1/2 1-5/8 1.481
2 2-1/8 1.959

Source: the rows "Outside" and "Inside" in the header of IFGC Table 402.4(9). The code tables are based on the Type K inside diameter, the smallest of the copper tube types, and the calculator does the same whatever type you use. IFGC 403.4.3 requires copper tubing to be Type K or L of ASTM B88, or ASTM B280.

Pressure checks

  • The delivery pressure less the allowable drop must be at least the minimum inlet pressure you enter for the appliances (IFGC 402.6, UPC 1208.3.3). If it is not, no result is shown. IFGC Appendix A101 notes that most residential appliances need about 5 inches water column at the inlet. Use your rating plates. The result is the design pressure at the most remote appliance with every appliance at full input. It is not a measured pressure.
  • A minimum inlet pressure below 2 in. w.c. is not accepted. That limit is a typing error guard of this tool, not a code value. It catches a pressure typed in psi.
  • IFGC Appendix A101 also says that at minimum flow the pressure at the inlet of an appliance must not exceed the pressure rating of the appliance regulator, that this is seldom of concern where the source pressure is 1/2 psi (14 in. w.c.) or less, and that it should be verified for greater pressures. IFGC 410.1 requires a line pressure regulator where an appliance is designed to operate at a lower pressure than the supply pressure. The calculator shows a notice where the delivery pressure is above 14 in. w.c. If you enter the lowest maximum inlet pressure of your appliances and the delivery pressure is above it, no result is shown. The calculator does not select regulators.
  • The form offers the pressure drops for which the code publishes a low pressure natural gas table that the equation reproduces: 0.3 and 0.5 in. w.c. for steel pipe (IFGC Tables 402.4(1) and 402.4(2)) and 0.3 and 0.5 in. w.c. for copper tubing (Tables 402.4(8) and 402.4(9)). Any other drop is an engineering method that needs the approval of the code official.
  • A notice is shown where the delivery pressure is below 6 in. w.c., because UPC 1215.6 requires prior approval of such a design by the Authority Having Jurisdiction.

Selection and rounding

  • The smallest size in the table that passes both checks is selected.
  • The pass test uses unrounded numbers. Rounding is for display only.
  • Displayed capacity is rounded down to three significant digits and displayed load is rounded up. Where that would hide a pass, more digits are shown.
  • A section is flagged where its load is above 97 percent of the computed capacity, so that you recheck lengths, fittings and ratings.
  • The printed tables are rounded. The notes of the code tables say the entries are rounded to three significant digits. The computed capacity can therefore differ from the printed table value by up to half a unit of the last printed digit, in either direction. Where the printed value is the lower one, a load between the two passes the equation but is above the table. IFGC 402.3 allows sizing by the tables or by the equations, but someone who checks your work against the table may ask for the next larger size. The calculator flags a section where its load is above the capacity rounded the way the tables are rounded. It does not store the tables, so this flag is our own rounding of our own number.
  • Steel pipe smaller than 1/2 in. is never selected. The steel tables of the code start at 1/2 in. UPC 1214.4 sets 1/2 in. as the minimum size of the supply piping outlet for a gas appliance, and 3/4 in. for a mobile home. The calculator does not apply the mobile home minimum. It shows a notice where an outlet is smaller than 3/4 in., and another for copper smaller than 1/2 in.

How the computation is checked

The sizing code is covered by automated tests. They compare the computed capacity with a sample of 176 published values from IFGC Tables 402.4(2), 402.4(3) and 402.4(9), and each must agree within 0.51 of one unit in the last printed digit. They also rework the piping examples in IFGC Appendix A (Sections A106.1 and A106.3) and in UPC Figure 1215.1.1 and require the pipe sizes the codes print. A further sample of table cells checks the rounding flag and the handling of sizes the tables print as NA. The published tables are used only to check the computation. They are not stored in or shown by the calculator.

The inside diameters listed above are the working data of the calculator. They were read from the headers of the IFGC tables named under each list. The standards the code names for these products (ASME B36.10M for the dimensions of steel pipe in IFGC 403.3.2, ASTM B88 for copper tube in IFGC 403.4.3) were not opened for this tool.

What the tool does not do

  • Corrugated stainless steel tubing (CSST). The equations require smooth inside walls (IFGC 402.4). CSST is sized from the tables in the tubing manufacturer's installation instructions for the product and its EHD size.
  • Pressure at 1.5 psi and above, 2 psi systems and regulators. For steel pipe the published tables for 2 psi and 5 psi inlet pressure are lower than the high pressure equation at short lengths in our check, so the equation is not used. Use the code table for the pressure and material and the regulator manufacturer's data. Other operating pressures often need the approval of the code official and the gas utility (IFGC Appendix A103.2 and A103.3).
  • Propane (LP gas). The propane tables of the code are in thousands of Btu per hour, and the text we opened does not print the heating value behind them. Use the propane tables of the adopted code.
  • Polyethylene pipe, stainless steel tubing and other materials. Use the code tables or the manufacturer's data for the material.
  • Elevation above 2,000 ft. The code requires the flow rate to be adjusted for altitude (IFGC 402.2, UPC 1208.3.1). The sections we read do not give the method, so the calculator shows no result above that elevation.
  • Specific gravity other than 0.60. IFGC Appendix A102.4 says gas of 0.70 or less can be sized directly unless the code official specifies a gravity factor. For heavier gas ask the gas supplier.
  • Diversity factors. Every appliance is taken at full input.
  • Runs longer than 2,000 ft and loads beyond the listed sizes. These go to engineering methods acceptable to the code official (IFGC Appendix A101, UPC 1215.5).
  • The hybrid pressure method (IFGC 402.4.3) and the pressure drop per 100 feet method of Appendix A103.4.
  • Everything that is not pipe sizing: appliance connectors, meters, service piping, venting, combustion air, materials approval, support, testing and purging.
  • Local rules. The calculator does not know which code edition or amendments your jurisdiction has adopted.

Permit, inspection and test

Under the IFGC, an owner, the owner's authorized agent or a contractor who wants to install, alter, repair or replace an installation regulated by the code must first apply to the code official and obtain the required permit (IFGC 105.1). All piping installations are visually inspected and pressure tested before acceptance and initial operation (IFGC 406.1). State or local law sets what applies where you work and who may do the work.

Sources

NFPA 54 (National Fuel Gas Code) was not opened for this tool, so no NFPA 54 section is cited here. State and local amendments were not reviewed.

Gas pipe sizing sources checked on October 2, 2026.

Rolling offset

How the rolling offset calculator computes its results and where each take-out comes from. Sources were read on October 3, 2026 and re-read on October 4, 2026.

Formulas

Two parallel pipes joined by two fittings of the same angle θ, all lengths in one unit.

true offset = sqrt(rise to the power 2 + roll to the power 2)

travel = true offset ÷ sin θ

run = true offset ÷ tan θ (0 at 90°)

roll angle = atan2(roll, rise)

cut length = travel minus take-out 1 minus take-out 2

hub to hub minimum = socket depth 1 + socket depth 2

The two pipe axes are parallel, so the connecting piece lies in one plane with them. In that plane it is the hypotenuse of a right triangle whose legs are the true offset (the perpendicular distance between the axes) and the run. The fitting angle is the angle between the connecting piece and the pipe axis, hence travel = true offset ÷ sin θ and run = true offset ÷ tan θ. The roll does not change the fittings; it only turns the plane of the offset about the pipe axis by the roll angle. The tests check that run² + true offset² = travel², that the travel is never shorter than the true offset, and that swapping rise and roll changes only the roll angle.

For the preset angles the multipliers that follow from the formulas are: 22.5°: travel = 2.613126 × true offset, run = 2.414214 × true offset ; 45°: travel = 1.414214 × true offset, run = 1 × true offset ; 60°: travel = 1.154701 × true offset, run = 0.57735 × true offset ; 90°: travel = 1 × true offset, run = 0 × true offset . Any other angle above 0 and up to 90° can be typed.

Take-out

The take-out used here is the fitting's laying length: the distance from the intersection of the fitting's centre lines to the point where the pipe end stops inside the fitting. For a solder cup or a solvent weld socket that is the bottom of the socket, so the cut length is the length of pipe to cut with both ends fully seated. Charlotte Pipe's catalog defines its dimension G as the laying length, intersection of center lines to bottom of socket, for 90 degree elbows, tees and crosses, and J the same for 45 degree elbows, each ± 1/32 in. (DC-PR, page 6). NIBCO's catalog does not define its dimension letters in text; its page 11 drawings show DIM. C from the centre line to the inner shoulder of the cup, and that reading is a judgement of this tool (see the open items).

The calculator holds the catalog take-outs of six fitting patterns, as printed, in fractions of an inch. The pages show only the value for the size you pick, with its catalog page and tolerance; no catalog table is reproduced here.

  • Copper 45 degree elbow, wrot, solder cup, C x C (NIBCO 606). Sizes 1/2 to 4 in. Take-out: NIBCO Copper Fittings Catalog, page 11 (revised 8/10/2021), catalog dimension C, read as centre line to bottom of the cup; no tolerance is printed for dimension C. Standard named by the catalog: ASME B16.22, as stated in the NIBCO catalog specification text (page 4). Socket depth for the hub to hub check: Copper Tube Handbook (CDA A4015-26/24), Table 14.9, female end depth G minimum, wrought fittings.
  • Copper 90 degree elbow, close rough, wrot, solder cup, C x C (NIBCO 607). Sizes 1/2 to 4 in. Take-out: NIBCO Copper Fittings Catalog, page 11 (revised 8/10/2021), catalog dimension C, read as centre line to bottom of the cup; no tolerance is printed for dimension C. Standard named by the catalog: ASME B16.22, as stated in the NIBCO catalog specification text (page 4). Socket depth for the hub to hub check: Copper Tube Handbook (CDA A4015-26/24), Table 14.9, female end depth G minimum, wrought fittings.
  • PVC Schedule 40 45 degree elbow, socket x socket (Charlotte 417, part 2309). Sizes 1/2 to 8 in. Take-out: Charlotte Pipe Dimensional Catalog DC-PR (updated January 27, 2026), page 41, catalog dimension J, laying length, intersection of centre lines to bottom of socket; plus or minus 1/32 in.. Standard named by the catalog: ASTM D2466, as stated in the catalog section heading. Socket depth for the hub to hub check: Charlotte Pipe Dimensional Catalog DC-PR (updated January 27, 2026), page 6, table 'Schedule 80 and Schedule 40 Tapered Socket Dimensions', socket length C (minimum), Schedule 40 column.
  • PVC Schedule 40 90 degree elbow, socket x socket (Charlotte 406, part 2300). Sizes 1/2 to 8 in. Take-out: Charlotte Pipe Dimensional Catalog DC-PR (updated January 27, 2026), page 36, catalog dimension G, laying length, intersection of centre lines to bottom of socket; plus or minus 1/32 in.. Standard named by the catalog: ASTM D2466, as stated in the catalog section heading. Socket depth for the hub to hub check: Charlotte Pipe Dimensional Catalog DC-PR (updated January 27, 2026), page 6, table 'Schedule 80 and Schedule 40 Tapered Socket Dimensions', socket length C (minimum), Schedule 40 column.
  • PVC Schedule 80 45 degree elbow, socket x socket (Charlotte 817, part 8309). Sizes 1/2 to 8 in. Take-out: Charlotte Pipe Dimensional Catalog DC-PR (updated January 27, 2026), page 11, catalog dimension J, laying length, intersection of centre lines to bottom of socket; plus or minus 1/32 in.. Standard named by the catalog: ASTM D2467, as stated in the catalog section heading. Socket depth for the hub to hub check: Charlotte Pipe Dimensional Catalog DC-PR (updated January 27, 2026), page 6, table 'Schedule 80 and Schedule 40 Tapered Socket Dimensions', socket length C (minimum), Schedule 80 column.
  • PVC Schedule 80 90 degree elbow, socket x socket (Charlotte 806, part 8300). Sizes 1/2 to 8 in. Take-out: Charlotte Pipe Dimensional Catalog DC-PR (updated January 27, 2026), page 10, catalog dimension G, laying length, intersection of centre lines to bottom of socket; plus or minus 1/32 in.. Standard named by the catalog: ASTM D2467, as stated in the catalog section heading. Socket depth for the hub to hub check: Charlotte Pipe Dimensional Catalog DC-PR (updated January 27, 2026), page 6, table 'Schedule 80 and Schedule 40 Tapered Socket Dimensions', socket length C (minimum), Schedule 80 column.

Threaded, press, PEX, cast copper and DWV fittings, 22.5 and 60 degree fittings and every other brand are not in the table because no dimension table for them was opened. For those the take-out is typed in from the fitting in hand or from its catalog, and the result says so.

Checks and limits

  • The cut length is refused where it is 0 or negative (the fittings overlap). Where it is positive but shorter than two socket depths, the result is shown with a notice that the two hubs would touch.
  • The rise and the roll are accepted up to 10,000 in the unit chosen, a take-out up to 1,000, and the travel (so the run and the cut length too) up to 100,000; a fitting angle typed as a fraction of a degree turns a small offset into a travel beyond that and is refused with the angle named. Those limits are typing error guards of this tool, not code values. Angles are printed with enough decimals never to read as 0. Inches are shown with the nearest sixteenth beside the decimal; the fraction is display only and feeds nothing. Catalog take-outs are converted to millimetres at 25.4 mm per inch (NIST SP 811).
  • The computation is covered by automated tests against 20 worked examples (16 results and 4 refusals), the catalog take-outs and socket depths above, and the geometric identities listed under the formulas.

Open items

  • The reading of NIBCO's dimension C as the laying length to the cup bottom rests on the page 11 drawing and on a cup depth check: for a 1/2 in. 607 elbow, C of 11/32 in. plus the 0.50 in. cup depth of Copper Tube Handbook Table 14.9 gives about 0.84 in. centre to end, which fits a close rough wrot elbow. It has not been confirmed with NIBCO or on a measured fitting.
  • The PVC socket depths come from the catalog DC-PR (updated January 27, 2026), page 6, the same document as the take-outs. Charlotte's older submittal FO-SUB-PVC-80 (5-30-19) prints the same table and agrees in every cell but one: Schedule 80, 1 1/4 in., where the submittal prints 1.250 in. and the catalog 1.290 in. Both were re-read on October 4, 2026; the calculator uses the current catalog. The difference moves the hub to hub notice for that one size by 0.08 in. and changes no cut length.
  • Charlotte's Schedule 40 45 degree elbow prints a J of 5/16 in. for 1 in., smaller than the 11/32 in. for 3/4 in. The value is used as printed.
  • The standards the catalogs name (ASME B16.22, ASTM D2466, ASTM D2467) and any threaded fitting standard (ASME B16.3) were not opened. The take-outs are catalog values of one brand and pattern; another brand's fitting can differ.

Sources

Not opened: ASME B16.22, ASTM D2466, ASTM D2467 and ASME B16.3. Nothing on these pages is attributed to them.

Rolling offset sources read on October 3, 2026, re-read on October 4, 2026.

Pipe volume

How the pipe volume calculator computes its results and where each inside diameter comes from. Sources were read on October 3, 2026 and re-read on October 4, 2026.

Formulas

area (in²) = π ÷ 4 × ID to the power 2

volume (in³) = area × length (in.), with length (in.) = ft × 12 = m × 1,000 ÷ 25.4

gallons = volume ÷ 231

litres = gallons × 3.785412

weight (lb) = gallons × 8.34; weight (kg) = litres × 0.99975

ID is the inside diameter in inches. Volumes are shown to three significant digits and weights to the nearest tenth; the computation uses the unrounded numbers. Fittings and valves are not added.

Constants

Inch
25.4 mm exactly. NIST SP 811 Appendix B.8: inch = 2.54 E-02 m.
Cubic inches per gallon
231. NIST SP 811 Appendix B.8: gallon (U.S.) = 3.785 412 E-03 m³ and cubic inch = 1.638 706 E-05 m³; 3.785412 E-03 ÷ 1.638706 E-05 = 231.00.
Litres per gallon
3.785412. NIST SP 811 Appendix B.8.
Weight of water
8.34 lb per gallon. The USGS water density table gives 62.408 lb per cubic foot at 50°F; 62.408 × 231 ÷ 1,728 = 8.343 lb per gallon, rounded to two decimals. For comparison the same table gives 62.424 at 39.2°F (8.345 lb per gallon) and 62.300 at 70°F (8.329), and the federal water heater test method uses 8.24 lb per gallon at 125°F. The tool weighs cold water and says so.
Density
0.99975 kg per litre. USGS water density table: 0.99975 g/cm³ at 50°F.

Inside diameters

The inside diameters are the working data of the calculator. They were read from the documents below, which name the product standards; the standards themselves (ASME B36.10M, ASTM B88, ASTM D1785, ASTM F876) were not opened. The calculator shows only the value for the size you pick, with its source; no dimension table is reproduced here.

  • Steel, 1/2 in. Schedule 80. The Wheatland brochure prints an inside diameter of 0.549 in., but its outside diameter 0.840 in. minus two walls of 0.147 in. is 0.546 in., and its own metric column prints 13.9 mm (0.547 in.). Every other row equals OD minus two walls. On October 4, 2026 the row was cross checked against an independent table of ANSI/ASME B36.10M-1995 dimensions (Engineers Edge, Schedule 80 steel pipe), which prints 0.546 in. for 1/2 in. and agrees with the brochure in every other Schedule 80 row; the brochure also carries other misprints the calculator does not use (its 5 in. Schedule 40 row prints 158.2 mm for an inside diameter of 5.047 in., which is 128.2 mm). The calculator uses 0.546 in. and says so in the result. The difference is 1.1 percent of the volume. The standard itself was not opened.
  • PVC. The Charlotte sheets print the average outside diameter and the minimum wall. OD minus two minimum walls is the largest bore the standard allows, so PVC volumes are upper bounds, and the result says so. No opened source prints an average bore for PVC.
  • PEX. Two columns are offered. The listed column is the inner diameter printed on one manufacturer's data sheets (Uponor AquaPEX), named on the page because other brands list slightly different values. The SDR 9 column is derived: the public scope of ASTM F876-24 says the tubing is outside diameter controlled and made in nominal SDR9 dimension ratios, and with wall = OD ÷ SDR the bore is OD × 0.777778. The ASTM text that defines a dimension ratio (ASTM F412) was not opened, so that step is labelled derived and the listed column is the page default.
  • Copper Tube Handbook volume column. The handbook also prints a volume per linear foot. Our bore based figure reproduces it within 0.37 percent for every size except two cells that appear to be misprints: Type L 5/8 in. prints .0174 gal per ft, the Type K figure (the Type L bore gives .0181), and Type L 4 in. prints .571 gal per ft where its own cross section of 12.0 in² gives .623. The handbook column is used only as a loose check in the tests (within 0.5 percent, those two rows excluded); the bore based value is the tool's value.

Checks and limits

  • Automated tests cover 17 worked examples (14 results and 3 refusals) to six significant digits, every inside diameter above against the fixture file, the PVC bores as OD minus two walls, the PEX SDR bores, and 32 rows of the Copper Tube Handbook volume column. A cross check against a different document: Wheatland's A53 Schedule 40 submittal prints 2 in. pipe at 3.66 lb per ft empty and 5.109 lb per ft water filled, 1.449 lb of water per foot; the calculator gives 1.454, 0.3 percent apart.
  • The length is accepted from 0.001 ft (0.0003 m) up to 100,000 ft (30,480 m). Both limits are typing error guards of this tool; the lower one also keeps a vanishingly small length from reaching the display formatter. Sizes not read from a source are not offered.
  • Not covered: fittings and valves, partly filled or sloped drains, CPVC, ABS, cast iron, copper DWV and ACR tube, steel above 4 in. or below 1/2 in., PVC above 6 in., and hot water weight.

Sources

Not opened: ASME B36.10M, ASTM B88, ASTM D1785, ASTM F412 and the ASTM F876 dimension tables. Nothing on these pages is attributed to them.

Pipe volume sources read on October 3, 2026, re-read on October 4, 2026.

Tankless water heater sizing

How the tankless water heater sizing calculator computes the input a heater needs, and where each constant and preset comes from. Sources were read on October 3, 2026 and re-read on October 4, 2026.

The result is an input requirement: the heat the water needs at the flow and temperature rise entered, divided by the efficiency entered. It is for comparison with the manufacturer's flow versus temperature rise data for a unit. The tool does not pick a model or a brand.

The heat equation

Heat added to flowing water is mass per hour × specific heat × temperature rise.

heat (Btu/h) = K × flow (gpm) × rise (°F)

K = 60 min/h × 8.34 lb/gal × 1.00 Btu/(lb·°F) = 500.4 Btu/h per gpm per °F

fuel input (Btu/h) = heat ÷ efficiency

electrical input (kW) = fuel input ÷ 3,412

rise (°F) = set point minus incoming temperature; flow (gpm) = sum of count × gpm of each fixture

Constants

Weight of a gallon of water, 8.34 lb
USGS water density table: 62.408 lb per cubic foot at 50°F; × 231 in³ per gallon ÷ 1,728 in³ per cubic foot = 8.343, rounded to 8.34. The gallon and the cubic inch are from NIST SP 811 Appendix B.8 (see the pipe volume section).
Specific heat, 1.00 Btu/(lb·°F)
10 CFR 430 Subpart B Appendix E, sections 6.3.9 and 6.4.5: Cp = 1.00 Btu/(lb °F), the specific heat of water at 91.5°F.
Alternative density, 8.24 lb/gal
The same sections of Appendix E use ρ = 8.24 lb/gallon, the density of water at 125°F. With it K = 494.4, 1.2 percent below 500.4. The tool uses 500.4, the cold water figure and the larger input, and shows the alternative in its math block for reference.
Btu per kWh, 3,412
Appendix E, section 6.3.5: electrical energy is converted to thermal energy at 1 kWh = 3412 Btu.
Federal test conditions, 58°F in, 125°F out, 67°F rise
Appendix E, section 2.3 (supply water 58°F ± 2°F), sections 2.4 and 2.5 (outlet and set point 125°F ± 5°F) and section 6.3.9 (67°F nominal rise). They are laboratory test conditions, so the form does not prefill them. A result computed at exactly those conditions carries a notice saying so.
Efficiency
The number the equation needs is the steady state ratio of heat into the water to fuel input, which Appendix E section 1.11 calls recovery efficiency: the ratio of energy delivered to the water to the energy content of the fuel consumed. The Uniform Energy Factor (UEF) printed on consumer product pages is the result of the 24 hour simulated use test of Appendix E and includes standby and cycling losses, so it is not the same quantity; using it is an approximation that slightly overstates the input. The field takes the thermal efficiency from the manufacturer's specification sheet and has no default. It accepts 0.50 to 1.00.

Fixture flow presets

Each preset is labelled with its source beside the field, and a preset can be overwritten with the rate marked on the fixture. The federal maxima are the largest flow a conforming fixture can pass at the test pressure; the IPC Table 604.3 figures are the minimum the distribution system must deliver at the outlet. Counting the full fixture flow as hot water is the conservative choice (see the mixed fixture note). A clothes washer or anything else without a preset is typed in; no opened source prints a figure for it.

  • Showerhead, federal maximum: 2.5 gpm, a maximum flow. 10 CFR 430.32(p): 2.5 gpm at 80 psi flowing pressure, showerheads manufactured after January 1, 1994.
  • Showerhead, 2024 IPC maximum: 2 gpm, a maximum flow. 2024 IPC Table 604.4: shower head 2.0 gpm at 80 psi (footnote c, ASME A112.18.1-2020/CSA B125.1 high efficiency).
  • Lavatory faucet, private: 2.2 gpm, a maximum flow. 10 CFR 430.32(o): lavatory faucets 2.2 gpm at 60 psi; 2024 IPC Table 604.4 lavatory, private, 2.2 gpm at 60 psi.
  • Kitchen (sink) faucet: 2.2 gpm, a maximum flow. 10 CFR 430.32(o): kitchen faucets 2.2 gpm at 60 psi; 2024 IPC Table 604.4 sink faucet 2.2 gpm at 60 psi.
  • Lavatory faucet, public, other than metering: 0.5 gpm, a maximum flow. 2024 IPC Table 604.4: lavatory, public (other than metering) 0.5 gpm at 60 psi.
  • Bathtub filler: 4 gpm, a design flow at the supply outlet. 2024 IPC Table 604.3: bathtub, balanced pressure, thermostatic or combination mixing valve, 4 gpm at 20 psi.
  • Laundry tray: 4 gpm, a design flow at the supply outlet. 2024 IPC Table 604.3: laundry tray 4 gpm at 8 psi.
  • Dishwasher, residential: 2.75 gpm, a design flow at the supply outlet. 2024 IPC Table 604.3: dishwasher, residential 2.75 gpm at 8 psi.
  • Sink, residential, design flow: 1.75 gpm, a design flow at the supply outlet. 2024 IPC Table 604.3: sink, residential 1.75 gpm at 8 psi (the faucet maximum in Table 604.4 is 2.2 gpm).

Set point notices

  • 2024 IPC 412.3 requires individual shower and tub shower combination valves to limit the maximum setting to 120°F, and 412.5 the same for the water temperature limiting device of a bathtub. The form prefills 120°F. A set point above it still computes, with a notice that those fixtures need the limiting valves the code requires. The code adopted where you work governs.
  • 2024 IPC Chapter 2 defines hot water as water at 110°F or more and tempered water as 85°F to 110°F. A set point below 110°F shows a notice that the water is not hot water as the IPC defines it.

Mixed fixtures

A shower is mixed at the valve. With a set point T, incoming temperature C and mix temperature M, the hot share of the fixture flow is (M minus C) ÷ (T minus C), an energy balance. The heat the heater adds is the same either way: K × total flow × (M minus C) = K × hot flow × (T minus C). With 2.5 gpm, a 105°F mix, a 120°F set point and 50°F incoming water the hot share is 0.7857, the hot flow 1.964 gpm, and the heat 68,805 Btu/h both ways; the tests check this identity. The tool takes no mix temperature. It counts the full fixture flow at the set point rise, which is the larger flow for the manufacturer's rise chart and never understates the heat.

Incoming water temperature

The incoming temperature is a user input, accepted from 33 to 90°F (a typing error guard of this tool; a value typed in Celsius is the usual cause of a refusal). No current federal or state table of incoming or ground water temperature was found when this tool was built; the DOE Energy Saver pages on water heater sizing returned 404 on October 3, 2026 and nothing is attributed to them. The one public source opened is USGS Water-Supply Paper 520-F (1925), which the page offers as hints:

  • Ground water from wells 20 to 200 ft deep is about 3 to 6 °F above the mean annual air temperature of the place (WSP 520-F, pages 97 to 98).
  • Plate VIII, "Approximate temperature of water from nonthermal wells at depths of 30 to 60 feet", draws contours at 37, 42, 47, 52, 57, 62, 67, 72, 77°F. The page reads them as bands: 37°F along the northern border (Montana, North Dakota, Minnesota, northern Maine); 42°F across the northern tier and northern New England; 47°F through Minneapolis, Milwaukee, Detroit and Boston; 52°F through Omaha, Chicago, Cleveland, New York and Salt Lake City; 57°F through Kansas City, St. Louis, Washington and San Francisco; 62°F through Oklahoma, Tennessee, North Carolina, Virginia and Los Angeles; 67°F through Dallas, Birmingham, Atlanta, Charleston and southern Arizona; 72°F along the Gulf coast, north Florida and the lower Colorado River; 77°F in south Florida.
  • The map is from 1925, drawn from the air temperature normals of that time, and is generalized. Surface water supplies vary by season; the paper gives 32 to 34 °F as the minimum in the coldest months. Measure the cold water at the job in winter, when sizing matters most.

Checks and limits

  • Automated tests cover 15 worked examples (10 results within 1 Btu/h and 0.001 kW, 5 refusals), the nine presets, the mixed fixture identity, proportionality to flow, rise and 1 ÷ efficiency, and every range above. The constant K and its 494.4 alternative are derived in the tests from the stored density and specific heat, not copied.
  • Counts from 1 to 20 of each fixture, flows from 0.1 to 15 gpm each, a total up to 30 gpm, and a set point from 100 to 150°F. Those limits are typing error guards of this tool; above 30 gpm the job is commercial sizing, which the tool does not cover.
  • Not covered: choosing a model or brand, the unit's own flow limit at the computed rise, gas pipe sizing, venting, combustion air, condensate, electrical service and wire size, recirculation, demand by number of occupants, water pressure, and storage, hybrid or solar heaters.

Sources

Not opened: the 2024 Uniform Plumbing Code (for this tool), any current table of incoming water temperature by state, and the DOE Energy Saver pages, which returned 404. Nothing on these pages is attributed to them.

Tankless sources read on October 3, 2026, re-read on October 4, 2026.

Drainage fixture units and drain sizing

How the drainage fixture unit calculator rates fixtures, adds them up and picks a pipe size, where each rule comes from, and what it leaves out. The sources were first read on October 3, 2026 and every cited section and table cell was re-read on October 4, 2026.

Scope

  • Gravity sanitary drainage inside one building, sized by drainage fixture units under the 2024 International Plumbing Code (IPC) or the 2024 Uniform Plumbing Code (UPC), one code at a time. The two codes rate some fixtures differently and are not mixed.
  • Horizontal branches, stacks, the building drain and its branches, and a building sewer up to 6 in. Pipe sizes 1-1/4 in. to 6 in. Larger pipe is refused.
  • 40 IPC fixture rows and 48 UPC fixture rows, including fixtures not listed by name, which the codes rate by their trap or outlet size, and pumped or continuous discharges entered in gallons per minute.

Fixture units

  • IPC. Each fixture takes the value of its row in Table 709.1. A bathroom group is one row, and fixtures added to the group are added at their own value (Table 709.1 note f). Water closets and urinals are rated by flush volume and by private or public use. Fixtures not listed are rated by the size of their fixture drain or trap from Table 709.2 (Section 709.2). A discharge known only in gallons per minute counts 2 fixture units per gpm (Section 709.3). A receptor that receives only clear water from display cases, ice bins, coolers and freezers counts one half (Section 709.4.1). Floor sinks and other indirect waste receptors are not rated by the tool, because their load is the sum of the fixtures that drain to them (Section 709.4, note h); enter those fixtures instead.
  • UPC. Each fixture takes the value of its row in Table 702.1 in the private, public or assembly column; assembly is public use in an assembly occupancy per Table 422.1 (note 8). Where the table prints a dash for that occupancy the tool refuses the fixture in that column rather than guessing. Fixtures not listed are rated by the size of their trap and trap arm from Table 702.1(1) (Section 702.1). Clothes washers in a battery of 3 or more count 6 units each on the common piping (note 5). Continuous flow from a pump, ejector or similar device counts 2 units per gpm (Sections 702.3 and 710.5).
  • Intermittent flow under the UPC. Table 702.2 rates an intermittent discharge by gpm band, up to 50 gpm, and gives far fewer units than the continuous rule. The sizing module computes it and the tests cover it, but the form offers only the continuous rating, because the choice can make an undersized drain look acceptable and belongs to the Authority Having Jurisdiction. A result that includes a continuous discharge shows the other reading in a notice.
  • Half units are summed exactly. Display rounding never feeds back into a computation. Only the single table cells that decide one result appear on the page, in the math of that section; the tables themselves are not reproduced.

Which table sizes which pipe

  • IPC. The building sewer, the building drain and horizontal branches of the building drain are sized from Table 710.1(1) at the slope you choose; a dash in that table means the size is not available at that slope, which agrees with the minimum slopes of Table 704.1. Because 1/16 in. per ft is a dash for every size through 6 in. and Table 704.1 allows it only for 8 in. and larger, that slope is refused for the slope itself, whatever the load, with those two tables named. Horizontal branches that drain to a stack, and stacks, are sized from Table 710.1(2) (Section 710.1). The two tables give different sizes for the same load, so the tool asks what a branch connects to and, where the other table would read differently, says so in a notice.
  • IPC stacks. The load discharged into one branch interval is checked against the one branch interval column, and the total load against the column for three branch intervals or less or for more than three (Table 710.1(2) note b). Branches are grouped into intervals by the interval number you enter, counted from the top; copies of a numbered branch take consecutive intervals below it. Every branch left without a number, with all its copies, and any fixture entered directly on the stack, is taken as connecting in one and the same branch interval. That is the most conservative reading of the table: the one interval column sees their combined load and the total column stays the three or less column. The result names that assumption in a notice and shows the size the other reading, one interval per unnumbered connection, would give. The stack is shown as one size for its full height; the reduction toward the top that note b allows is not performed. Vertical stack offsets are sized as the stack (Section 710.1.2) and horizontal offsets as a building drain (Section 710.1.1); the tool does not model offsets and shows a notice where a stack has more than four branch intervals (Section 711).
  • UPC. Every horizontal drain, building drain and building sewer up to 6 in. is sized from the horizontal row of Table 703.2, and every stack from the vertical row together with the maximum vertical length row (Sections 703.1 and 703.2). The table has no branch interval column, so the tool uses the total load and the developed length of the stack. A stack longer than the maximum length of 6 in. needs a larger size whatever its load, and is refused for its length with the 8 in. row of Table 703.2 and Section 703.1 named. Building sewers 8 in. and larger have maximum and minimum loadings per slope in Table 717.1 and are refused. Where no size through 6 in. passes, the refusal repeats the reasons the 6 in. row failed on, and says the load is the cause only where a cell was exceeded.
  • Slope. Under the IPC the slope picks the column of Table 710.1(1). Under the UPC horizontal drainage piping is laid at 1/4 in. per ft (Sections 708.1 and 718.1); 1/8 in. per ft is offered only for the building drain, piping 4 in. and larger when first approved by the Authority Having Jurisdiction (Section 708.1), and for the building sewer, 4 through 6 in. where approved (Section 718.1), with the horizontal cells multiplied by 0.8 (Table 703.2 note 5) and a notice about the approval. A horizontal branch is 1/4 only, because the sections read give it no exception.

Rules applied to every section, each named in the result

  • Load against the table cell. Sizes are tried from the smallest up, and the first whose cell is not less than the load carried, and that no table note excludes, is the size by the table.
  • UPC table notes. No sink, urinal or dishwasher exceeding 1 fixture unit on 1-1/2 in. (Table 703.2 note 2); no water closet or six unit trap on 2 in. (note 3); not more than 6 water closets or 5 six unit traps on 3 in. (note 4); up to 8 public lavatories on a 1-1/2 in. vertical branch or horizontal sanitary branch sloped at 1/4 in. per ft (note 7, in the note's own words), applied only to the Lavatory row and only to a horizontal branch that drains to a stack at 1/4 in. per ft and carries nothing else. The note names branches, so a stack, the building drain and the building sewer never take it, and this tool has no vertical branch kind. A fixture rated six units or more that is not a water closet is taken as a six unit trap.
  • Water closet minimum. A pipe that carries a water closet is not smaller than 3 in. For the building drain and its branches that is a printed rule, IPC Table 710.1(1) note a. For branches and stacks it is a rule of this tool, and the result labels it so: the IPC prints no such minimum there, but the water closet trap matches the 3 in. fixture outlet (Table 709.1 note d) and Section 425.4 accepts a 3 in. closet bend as the smallest it names, and Section 704.2 forbids a reduction in the direction of flow, so the branch or stack downstream of a water closet is shown at 3 in. or larger. Under the UPC it follows from Table 702.1, which gives every water closet a 3 in. trap, with Table 703.2 note 3. No rule limiting the number of water closets on a 3 in. drain was found in the 2024 IPC Chapter 7, and the UPC limit is the six of note 4. A limit of two water closets on 3 in. appears only in UPC Appendix C, which applies only where adopted (Section 102.8) and which the tool does not apply.
  • Trap size. A pipe is not smaller than the largest minimum trap of the fixtures connected to it (IPC Table 709.1 and Section 1002.5, a trap is not larger than the drain it discharges into; UPC Table 702.1 and Section 1003.3, the trap equals the trap arm). UPC rows marked with note 2 get a 2 in. minimum drain.
  • Clothes washer standpipe (IPC Section 406.2). The trap and fixture drain are 2 in. and the fixture branch or stack that receives them is 3 in. or larger.
  • No reduction in the direction of flow. A section is never smaller than any section that discharges into it. The IPC states this in Section 704.2. No sentence to that effect was found in UPC Chapter 7; under the UPC the tool enforces it as its own rule, following from Section 703.1 (every pipe is sized for the total units connected) and Section 717.1 (no building sewer smaller than the building drain), and the result says so.
  • Within 1 fixture unit. A section whose load is within 1 unit of its cell is flagged so that you recheck the fixture list and the occupancy class.

What the tool does not do

  • Vents and vent stacks, trap arm lengths, cleanouts, fittings and changes of direction (UPC Section 706).
  • Combination waste and vent systems, wet vents, circuit vents and single stack systems.
  • Building sewers 8 in. and larger (UPC Table 717.1, IPC Section 708.1.2), stack offsets in buildings of five stories or more (IPC Section 711), and stack reduction toward the top (IPC Table 710.1(2) note b).
  • Indirect waste receptors, grease and oil interceptors, sumps, ejectors and pumps beyond converting their flow to fixture units, septic tank sizing (UPC Table 702.1 note 6, Appendix H), and storm or combined drainage.
  • Any appendix of either code, the International Residential Code, editions other than 2024, and state and local amendments. Future fixtures count only if you enter them (IPC Section 710.2).

How the computation is checked

Automated tests compare the working data of the sizing module with every fixture unit entry and every capacity cell of IPC Tables 709.1, 709.2, 710.1(1) and 710.1(2) and UPC Tables 702.1, 702.1(1), 702.2, 703.2 and 717.1, recorded as test fixtures and never shown on a page. They rework seven layouts constructed from those tables (none is an example printed in a code), check the edges of the cells, the notes and the slope rules, run several hundred random layouts for the properties that sizes never decrease toward the sewer, loads add up and no dash cell is ever selected, and drive the real page in a test browser for the branch question, the occupancy selector, the links and the printed layout.

Permit and inspection

Under the IPC an owner, the owner's authorized agent or a contractor who wants to install, alter, repair or replace a plumbing system first applies to the code official and obtains the required permit (Section 105.1), and the work is inspected underground, at rough in and at final (Section 111.2). Under the UPC it is unlawful to install, alter, repair, replace or remodel a plumbing system without a plumbing permit, except exempt work (Section 104.1), and no plumbing system is covered, concealed or put into use until inspected and approved (Section 105.1). Licensing is determined by the Authority Having Jurisdiction (UPC Section 103.3.1) and by state law.

Sources

  • 2024 International Plumbing Code, Chapter 7 (ICC Digital Codes, Version 2.0). Sections 704.1, 704.2, 704.3, 704.4, 708.1.2, 709.1 to 709.4.1, 710.1, 710.1.1, 710.1.2, 710.2, 711.1 to 711.3, 713; Tables 704.1, 709.1 with notes a to h, 709.2, 710.1(1) with note a, 710.1(2) with notes a to c. The first printing of June 2023 was compared cell by cell with Version 2.0 and found identical in these tables.
  • 2024 International Plumbing Code, Chapter 2. Definitions of bathroom group, branch interval, building drain, building sewer, developed length, drainage fixture unit, fixture branch, fixture drain, horizontal branch drain, horizontal pipe, private, public, stack and vertical pipe.
  • 2024 International Plumbing Code, Chapter 4. Sections 406.2, 413.3, 413.4 and 425.4.
  • 2024 International Plumbing Code, Chapter 10. Section 1002.5.
  • 2024 International Plumbing Code, Chapter 1. Sections 101.2 with its exception, 101.2.1, 101.3, 102.1, 102.9, 102.10, 104.1, 105.1 and 111.2.
  • 2024 Uniform Plumbing Code (IAPMO read only viewer, Thirtieth Edition, first printing February 2023). Chapter 7 Sections 702.1, 702.2, 702.3, 703.1, 703.2, 703.3, 708.1, 710.5, 717.1 and 718.1 with Tables 702.1 and its notes 1 to 9, 702.1(1), 702.2, 703.2 and its notes 1 to 7, and 717.1 (printed pages 131 to 141); Chapter 2 definitions of bathroom group, building drain, building sewer, fixture unit, horizontal branch, horizontal pipe, private or private use, public or public use, trap arm and vertical pipe; Sections 101.3, 102.8, 103.1, 103.3.1, 104.1, 105.1, 105.4, 301.5 and 1003.3; Appendix C Section C 201.1. The values were taken from the viewer text layer and checked on the viewer page images on October 3, 2026.

Not opened: the 2024 International Residential Code Chapter 30, which most states apply to one and two family dwellings (IPC Section 101.2 exception); the 2021 and earlier editions of either code; state and local amendments; the fixture and pipe product standards the codes name. Nothing from them is used.

Drainage sources first read on October 3, 2026, re-read on October 4, 2026.