In short: the flow a gravity drain pipe can carry depends on its diameter, slope, roughness and how full it's running, via Manning's equation. A 4-inch PVC drain at a 2% slope, running half full, carries about 87 GPM — and, running completely full, exactly double that at the same velocity. Use the calculator above for your exact pipe and fill depth.
These figures are planning aids based on Manning's equation. For code-required drain sizing, confirm with a licensed engineer or your local plumbing code.
How to calculate gravity drain flow
Manning's equation predicts open-channel and partially full pipe flow from the cross-sectional area, the hydraulic radius, the slope and a roughness coefficient:
For a circular pipe that isn't flowing full, the tricky part is finding A and R at a given depth. This calculator uses the standard circular-segment geometry: for a pipe of diameter D flowing to depth y, the wetted angle is θ = 2·arccos(1 − 2y/D), the flow area is A = (D²/8)(θ − sin θ), and the wetted perimeter is P = (D/2)θ, giving R = A/P.
Worked example. A 4-inch PVC drain (n = 0.009) at a 2% slope, flowing half full: D = 0.1016 m, y = 0.0508 m, so θ = π exactly, A = 0.00811 m², P = 0.1597 m, R = 0.0254 m (1 in). Plugging into Manning's equation gives Q ≈ 0.00551 m³/s, which converts to 87.2 GPM at a velocity of 4.46 ft/s — the calculator's default result.
A neat property of circles. At exactly half full, a circular pipe's hydraulic radius equals its hydraulic radius when completely full (R = D/4 in both cases). Since velocity depends only on R, S and n, a half-full pipe flows at exactly the same velocity as a full one — only the flow rate is different, because only the area has changed. Slide the depth control above to 100% and watch the velocity row hold steady while the flow rate doubles.
Why diameter, slope and material change the answer
Diameter has the largest effect. Both the area and the hydraulic radius grow with diameter, so full-pipe capacity increases roughly with diameter to the 8/3 power — stepping from a 4-inch to a 6-inch drain roughly triples its capacity at the same slope.
Slope acts more gently. Flow rises only with the square root of slope, so doubling the slope raises capacity by about 41%, not 100%. Still, code minimum slopes exist for a reason — too flat, and both capacity and self-cleansing velocity fall short.
Material roughness sets a fixed multiplier. Since Q is directly proportional to 1/n, switching from smooth PVC (n = 0.009) to corrugated HDPE (n = 0.024) cuts capacity to roughly 38% of the smooth-pipe figure at the same size and slope — a large, often underestimated effect. See the channel flow calculator for the same equation applied to open channels, and the culvert flow calculator for larger culvert crossings with inlet-control checks.
Reference: full-pipe capacity (PVC/ABS, n = 0.009)
Flow capacity in GPM when running completely full, by pipe diameter and slope. Every value matches what the calculator returns at 100% depth for the same inputs.
| Diameter | 1% slope | 2% slope | 4% slope |
|---|---|---|---|
| 2 in | 19.4 | 27.5 | 38.9 |
| 3 in | 57.3 | 81.0 | 114.6 |
| 4 in (common house drain) | 123.4 | 174.5 | 246.8 |
| 6 in | 363.8 | 514.4 | 727.5 |
| 8 in | 783.4 | 1,107.9 | 1,566.8 |
| 10 in | 1,420.4 | 2,008.7 | 2,840.7 |
Worked examples
4-inch house drain, half full
87.2 GPM
PVC, 2% slope, running half full (the calculator's default) — the design-flow figure many drains are evaluated against. Velocity: 4.46 ft/s.
Same drain, running full
174.5 GPM
The same 4-inch PVC pipe at 100% depth carries exactly double the half-full flow — and the velocity is unchanged, at 4.46 ft/s.
4-inch drain at minimum slope
125.9 GPM
PVC at the IPC minimum of 1/8 in/ft (1.04%), running full: capacity drops to about 126 GPM at 3.21 ft/s — still above the 2 ft/s self-cleansing guideline.
What this calculator doesn't include
Fittings, transitions and entrance losses. Manning's equation describes steady, uniform flow along a straight run. Bends, junctions and changes in pipe size add local losses this tool does not account for.
Surcharged (pressurized) flow. Once a drain runs completely full and backs up above the pipe crown, it stops behaving like a gravity drain and starts behaving like a pressurized pipe — at that point, use the friction loss calculator instead.
Peak flow factors and pipe sizing rules. Actual drain sizing also considers fixture unit loads, code-mandated minimum sizes, and venting requirements — see the drain pipe size calculator and drainage fixture unit calculator for that side of the design.
Frequently asked questions
What is gravity drain flow?
Gravity drain flow is the movement of water through a pipe that is not pressurized — the water flows because the pipe slopes downward, not because a pump is pushing it. Sanitary drains, storm drains and most building drainage piping work this way. Manning's equation predicts how much flow a given pipe, slope and fill depth can carry.
Why doesn't a drain pipe flow completely full?
Drains are designed with air space above the water for venting, to avoid siphoning fixture trap seals, and to handle flow surges without backing up. Plumbing codes typically size sanitary drains around half full at design flow, reserving the rest of the pipe as freeboard for peak loads.
Is a half-full pipe's velocity the same as when it's full?
Yes, exactly — this is a well-known property of circular pipes in Manning's equation. At precisely half full, the hydraulic radius equals the same value as when the pipe is completely full, so the velocity is identical in both cases. Only the cross-sectional area (and therefore the flow rate) differs.
What is the minimum slope for a drain pipe?
The International Plumbing Code sets a common minimum of 1/4 inch per foot (about 2.08%) for drain pipes up to 2.5 inches in diameter, and 1/8 inch per foot (about 1.04%) for 3-inch and larger drains, though local codes and specific applications can vary. Flatter slopes reduce both flow capacity and self-cleansing velocity.
What velocity does a drain need to be self-cleansing?
A common rule of thumb in drainage design is a minimum velocity of about 2 feet per second at design flow, which is generally enough to keep solids in suspension and prevent them from settling and building up in the pipe. Flatter slopes, oversized pipes and low flows can all fall below this threshold.
How much does pipe material affect drain capacity?
Smoother materials carry more flow at the same diameter and slope. PVC and ABS, with a Manning's n around 0.009, are noticeably smoother than concrete, cast iron or vitrified clay at about 0.013, and far smoother than corrugated plastic pipe at around 0.024 — a corrugated pipe can carry roughly 30 percent less flow than smooth PVC of the same size and slope.
Sources & references
- Manning, R. (1891). On the flow of water in open channels and pipes. Transactions of the Institution of Civil Engineers of Ireland, 20, 161–207.
- International Code Council. International Plumbing Code (IPC), Chapter 7 — Sanitary Drainage.
- American Society of Civil Engineers (ASCE) & Water Environment Federation (WEF). Manual of Practice No. 9 — Design and Construction of Sanitary and Storm Sewers.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)