15.3 Slope, Fall & Grade

15.3 Slope, Fall & Grade

Quick Answer: Fall = slope × run. 1/4 in/ft × 40 ft = 10 inches of fall; 1/8 in/ft × 40 ft = 5 inches. 1/8 in/ft = 0.125 ÷ 12 = 1.04 percent grade. 248 CMR 10.15 Table 2 has no 1/8 in/ft column for a 3-inch building drain (40 DFU at 1/4, 48 at 1/2). 248 CMR 10.05 sets 1/4 in/ft minimum on horizontals 3 inches and smaller, and 1/8 in/ft minimum on pipe larger than 3 inches. Grade between two inverts is (invert difference) ÷ run. Invert is the lowest inside point of the pipe (248 CMR 10.03).

Part II will mix a tape-measure fall problem with a Massachusetts pitch rule. Independent OpenExamPrep teaching below is the math plus the 12/8/2023 table cell that forbids a 3-inch building drain at 1/8. Chapter 11.2 owns the full DFU columns; this section computes how far the invert drops and whether that pitch is a Table 2 option.

248 CMR 10.03 defines invert as the lowest point inside a pipe on which water can flow. Slope in that chapter points to grade. Grade is invert to invert, not dirt trench to dirt trench and not crown to crown. 248 CMR 10.05(2)(a) requires horizontal drainage to run in a straight practical line at a consistent uniform pitch. Do not steepen the last 10 feet to “make the invert” after laying 70 feet flat.

Formula table — fall, percent, inverts

Fall (inches) = (inches per foot) × run (feet).

Percent grade = (inches per foot ÷ 12) × 100, which is the same as (fall in feet ÷ run in feet) × 100.

1/8 in/ft to percent, written out: 1/8 = 0.125 inch of fall in 12 inches of run. 0.125 ÷ 12 = 0.0104167. × 100 = 1.04167 percent → 1.04%. As a fraction: (1/8) / 12 = 1/96 ≈ 1.04%. 1/4 in/ft: 0.25 ÷ 12 = 0.020833 → 2.08%. 1/2 in/ft: 0.50 ÷ 12 = 0.041667 → 4.17%.

Between two inverts:

• Fall in feet = upstream invert − downstream invert (when both are in feet).
• Fall in inches = fall in feet × 12.
• Inches per foot = fall in inches ÷ run in feet.
• Percent = (fall in feet ÷ run in feet) × 100.

If the downstream invert is higher, gravity flow on that run is gone. That is a 10.15(9) ejector problem, not a “negative 1/8” grade.

Massachusetts pitch, including the blank 3-inch 1/8 cell

248 CMR 10.05(2)(b): horizontal drainage 3 inches or smaller — minimum uniform pitch 1/4 inch per foot.

248 CMR 10.05(2)(c): horizontal drainage larger than 3 inches — minimum uniform pitch 1/8 inch per foot.

248 CMR 10.05(2)(d): a Massachusetts professional engineer may design a different pitch if computed velocity is not less than 2 feet per second. That is not a journeyman 1/8-on-3-inch shortcut.

248 CMR 10.05(2)(e) sends building-drain pitch to 10.15 Table 2. Table 2 (effective 12/8/2023) for building drains:

A 3-inch building drain cannot use 1/8 in/ft because the table has no cell and 10.05 already forbade that pitch on 3-inch and smaller pipe. You can still compute the fall of a 1/8 pitch — 40 ft × 0.125 = 5 inches — and then mark it illegal for that 3-inch building drain. The legal minimum pitch on that 3-inch horizontal is 1/4 in/ft, so the same 40 feet must fall 10 inches, and Table 2 will only load 40 DFU at 1/4 (or 48 at 1/2). Independently, the 10-foot foundation section of a building drain is still minimum 4 inch under 248 CMR 10.03. Do not punch a 3-inch building drain through the wall because 40 DFU “fits” the 1/4 column.

4-inch and larger may use 1/8 in/ft. That is when 180 DFU versus 216 DFU on a 4-inch building drain matters: 216 is the 1/4 column, not the 1/8 column. Chapter 11.2 drills that trap; here you only need it so a fall calculation at 1/8 on 4-inch pipe is a legal pitch if Table 2 load also fits 180 DFU.

Worked example 1 — Fall from a stated pitch (Quincy sewer run)

A 4-inch building sewer runs 36 feet at 1/4 in/ft.

Fall = 0.25 in/ft × 36 ft = 9.00 inches.

At 1/8 in/ft the same 36 feet would fall 0.125 × 36 = 4.50 inches. Four-inch pipe is larger than 3 inches, so 1/8 is a legal minimum pitch under 10.05; you still check Table 2 load (180 DFU at 1/8). If the stem switches the pipe to 3-inch, 4.50 inches is the fall of an illegal 1/8 pitch. The 3-inch run needs 9.00 inches at 1/4.

1/2 in/ft on 36 feet: 0.50 × 36 = 18 inches. That is a steep building drain; Table 2 allows more DFU at 1/2 (250 on 4-inch, 48 on 3-inch) because the water moves faster. Uniform pitch still means the whole 36 feet, not 18 inches of drop in the last 6 feet.

Worked example 2 — Convert 1/8 in/ft to percent, then use it

1/8 in/ft → percent: 0.125 ÷ 12 × 100 = 1.0417% → 1.04%.

A surveyor calls 1.04% on 80 feet of 4-inch sewer. Fall in feet = 0.010417 × 80 = 0.833 feet. Inches = 0.833 × 12 = 10.00 inches. Check the shop way: 1/8 in/ft × 80 ft = 10 inches. Percent and inches-per-foot agreed.

Wrong conversions: 0.125% (forgot to divide by 12 and multiply by 100 correctly), 12.5% (used 0.125 × 100 and skipped the 12 inches in a foot), 8% (wrote 1/8 as 8 percent). Those show up as distractors because they look like the 1/8.

2.08% is 1/4 in/ft, not 1/8. If an invert pair produces 2.08%, you are at 1/4, which is what a 3-inch horizontal needed anyway.

Worked example 3 — Grade between two inverts (Fall River)

Upstream invert 64.80 ft. Downstream invert 64.20 ft. Run 48.00 ft (horizontal distance along the pipe as given).

Fall = 64.80 − 64.20 = 0.60 ft = 0.60 × 12 = 7.2 inches.

Inches per foot = 7.2 ÷ 48 = 0.15 in/ft.

Percent = (0.60 ÷ 48) × 100 = 1.25%.

0.15 in/ft sits between 1/8 (0.125) and 1/4 (0.250). On a 4-inch building drain, 0.15 is steeper than the 1/8 minimum, so pitch is not the 10.05 problem; Table 2 load still uses the 1/8 column (180 DFU) only if you are actually at 1/8 — here the as-built grade is 0.15 in/ft, closer to 1/8 than to 1/4, and you do not get to claim the 216 DFU 1/4 column unless the invert drop is a true 1/4. This item asked for the computed grade, not a DFU upgrade.

If the same 0.60-foot drop is stretched over 80 feet: 7.2 ÷ 80 = 0.090 in/ft, which is flatter than 1/8 (0.125). Percent = 0.60/80 × 100 = 0.75%. That fails 10.05(2)(c) on pipe larger than 3 inches unless a PE designs ≥ 2 fps. Raising the upstream invert or lowering the downstream invert (or shortening the run) is how gravity comes back; wishing 1/8 onto the as-built numbers does not.

3-inch, 40-foot, 1/8 proposal: fall would be 40 × 0.125 = 5 inches. Table 2 still has no 1/8 cell for 3-inch building drain. Pitch it at 1/4: 40 × 0.25 = 10 inches of invert drop, load cap 40 DFU, and remember the through-wall building drain is still 4 inch under 10.03 for the foundation piece.

Official resources

• 248 CMR 10.05(2) (Cornell) — 1/4 in/ft on 3-inch and smaller; 1/8 in/ft on larger; PE 2 fps exception; pointer to Table 2
• 248 CMR 10.15 Table 2 (Cornell) — blank 3-inch 1/8 in/ft building-drain cell; 40 / 48; 4-inch 180 / 216 / 250
• 248 CMR 10.03 Definitions (Cornell) — invert; slope see grade; building drain 10-foot / 4-inch piece
• 248 CMR 10.00 Uniform State Plumbing Code (Mass.gov, effective 12/8/2023) — official PDF tables
• PSI Massachusetts plumbing Candidate Information Bulletin — Part II General Trade Calculations 5