Plumbing exam math comes in four flavors: slope and fall, fractions and decimals, volume and weight of water, and pressure versus height. None of it needs more than multiplication, but every flavor has a unit that is easy to mix up: inches per foot against feet, gallons against cubic feet, psi against feet of head. This guide gives the constants with their sources, then original practice problems with each step written out so you can check your own work against it.
Constants and where they come from
| Conversion | Basis | Value used in the problems |
|---|---|---|
| 1 foot | Definition: 12 inches | 12 inches |
| 1 cubic foot in gallons | Derived from NIST SP 811 factors (1 ft3 = 28.31685 L; 1 US gal = 3.785412 L): 7.4805 gal | 7.48 gallons (rounded) |
| 1 psi in feet of water | Derived from NIST SP 811 factors (1 psi = 6,894.757 Pa; 1 ft of water, conventional = 2,989.067 Pa): 2.307 ft | 2.31 feet (rounded) |
| 1 foot of water in psi | 1 / 2.307 = 0.4335 psi | 0.433 psi (rounded) |
| 1 gallon of water, weight | Physical approximation: water density varies with temperature; about 8.34 lb at ordinary room temperature | 8.34 pounds (approximate) |
Three kinds of numbers sit in that table: a definition (12 inches), factors derived from NIST SP 811 and then rounded the way exams usually round them, and one physical approximation (8.34 lb/gal). Keep them separate in your head: the rounding is a convention, the density is a property of water at a stated temperature. If a question supplies its own constant (for example, "use 7.5 gallons per cubic foot" or "8.33 pounds per gallon"), use the question's constant.
Slope and fall
Slope is stated in inches of drop per foot of horizontal run. Fall is the total drop over a run: fall = slope x run, with slope in inches per foot and run in feet, giving fall in inches. To express slope as a percentage, divide the inches of drop by 12 inches and multiply by 100.
Which slope applies depends on pipe size and on the code your state adopted. As one example of an IPC-based table, the New York City Plumbing Code (an adoption of the International Plumbing Code with local amendments) sets minimum slopes for horizontal drainage piping in its Table 704.1: 1/4 inch per foot for pipes 2-1/2 inches and smaller, 1/8 inch per foot for 3 through 6 inches, and 1/16 inch per foot for 8 inches and larger. We read those values in the NYC code text; check the IPC edition your state adopted, with its amendments, for the table that applies to you, and note that Uniform Plumbing Code jurisdictions use their own rule. On the exam, use the slope the question states or the table in the code the question names; the problems below state the slope so the arithmetic can be checked without a code book.
Problem 1: total fall
A 2-inch drain runs 32 feet horizontally at 1/4 inch per foot. What is the total fall?
Fall = 0.25 inch/ft x 32 ft = 8 inches. Unit check: (in/ft) x ft = in.
Problem 2: fall in feet, and an invert elevation
A 4-inch building drain starts at an invert elevation of 100.00 feet and runs 60 feet at 1/8 inch per foot. What is the invert elevation at the downstream end?
Fall = 0.125 in/ft x 60 ft = 7.5 inches. Convert to feet: 7.5 / 12 = 0.625 ft. Downstream invert = 100.00 minus 0.625 = 99.375 feet (99.38 rounded to hundredths). The two traps are subtracting 7.5 feet instead of 7.5 inches, and adding instead of subtracting; a drain falls in the direction of flow.
Problem 3: slope as a percentage
What percent grade is 1/4 inch per foot?
0.25 in / 12 in = 0.02083; x 100 = 2.08 percent. Likewise 1/8 inch per foot is 1.04 percent. If a choice says "2.5 percent," it came from dividing by 10 instead of 12.
Problem 4: run from a fall limit
A branch must drop no more than 6 inches between two points because of a framing constraint, and it must be laid at 1/4 inch per foot. What is the maximum horizontal run?
Run = fall / slope = 6 in / (0.25 in/ft) = 24 feet. Unit check: in / (in/ft) = ft.
Fractions, decimals, and feet-inches
Convert every fraction to a decimal before you multiply, and keep feet and inches separate until the last step.
Problem 5: a 45-degree offset
Two parallel horizontal pipes are 14 inches apart (center to center). A 45-degree offset connects them. What is the travel (the length of the diagonal piece, center to center), using 1.414 as the multiplier for a 45-degree offset?
Travel = offset x 1.414 = 14 x 1.414 = 19.8 inches (19.796). The 1.414 is the square root of 2, from the geometry of a 45-degree right triangle; questions usually supply it. If a question gives the travel and asks for the offset, divide instead: 19.8 / 1.414 = 14.
Problem 6: adding mixed measurements
Three pieces of pipe measure 3 ft 8 in, 5 ft 9 in, and 2 ft 11 in. What is the total length?
Feet: 3 + 5 + 2 = 10 ft. Inches: 8 + 9 + 11 = 28 in = 2 ft 4 in. Total: 12 ft 4 in. Carrying the inches into feet at the end, not during the addition, avoids the common slip of writing 10 ft 28 in.
Volume, gallons, and weight
Problem 7: gallons in a tank
A rectangular tank measures 4 ft by 3 ft by 2 ft deep. How many gallons does it hold when full, using 7.48 gallons per cubic foot?
Volume = 4 x 3 x 2 = 24 cubic feet. Gallons = 24 x 7.48 = 179.5 gallons (179.52). Unit check: ft cubed x (gal per ft cubed) = gal. Multiplying by 7.48 before converting inches to feet, when a dimension is given in inches, is the classic error; convert dimensions first.
Problem 8: weight of that water
What does the water in Problem 7 weigh, at 8.34 pounds per gallon?
179.5 x 8.34 = 1,497 pounds (1,497.0). Questions like this appear when supports or a floor load are the subject.
Pressure and height
Water pressure changes with elevation: every foot of height changes the static pressure by about 0.433 psi, and every psi corresponds to about 2.31 feet of water. Going up loses pressure; going down gains it.
Problem 9: pressure at an upper-floor fixture
The water pressure at the meter is 60 psi. A fixture is 46.2 feet above the meter. Ignoring friction loss, what is the static pressure at the fixture?
Loss = 46.2 ft x 0.433 psi/ft = 20.0 psi. Pressure at fixture = 60 minus 20 = 40 psi. Cross-check with the other constant: 46.2 / 2.31 = 20.0 psi. Same answer, which is the point of knowing both forms.
Problem 10: height from a pressure
A gauge at the base of a filled vertical pipe reads 26 psi. How tall is the water column?
Height = 26 psi x 2.31 ft/psi = 60.1 feet (60.06). Unit check: psi x (ft per psi) = ft.
The unit check, every time
- Write the unit the question wants.
- Write each number with its unit.
- Cancel units on paper; if the leftover unit is wrong, the setup is wrong.
- Compute; round only at the end and in the direction the question specifies.
Practice next
The Drainage and Vent Systems topic explains why slope matters for carrying solids, and the Water Supply topic covers the pressure and demand concepts behind Problems 9 and 10. Then take the free plumbing practice test with a calculator and write the unit check for every numeric question. For reading the drawings those numbers usually come from, see plumbing drawing questions.
Sources and verification notes
Gallons per cubic foot and psi per foot of water are derived from NIST SP 811 conversion factors and then rounded the way exams usually round them; the 8.34 pounds per gallon figure is a physical approximation for water at ordinary temperature, not a NIST factor. The slope table is cited to the New York City Plumbing Code's Section 704.1 and Table 704.1, which we read directly on September 18, 2026; the NYC code is an IPC adoption with local amendments, and the ICC's own 2021 IPC text was not read directly for this revision, so the guide does not claim to have verified the unamended model code. UPC jurisdictions differ. The problems state the slope to use rather than asserting a code minimum, and are original practice examples, not official exam questions.
- NIST Special Publication 811, Appendix B.8 (unit conversion factors)Checked September 18, 2026
- NIST Special Publication 811, Appendix B.8 (unit conversion factors)Checked September 18, 2026
- New York City Plumbing Code (IPC-based), Section 704.1 and Table 704.1, via American Legal PublishingChecked September 18, 2026
- International Code Council, 2021 International Plumbing Code, Section 704.1 (model code; full text behind the ICC viewer, not read directly for this revision)
Written by the ExamsLib editorial team. Practice examples in this guide are original and are not official exam questions. Exam rules change; the candidate bulletin from your licensing authority is the final word. Found an error? Contact us.
