In short: a 24-inch concrete culvert on a 1% slope carries about 22.6 cfs (10,150 gpm) when flowing full, at a velocity of roughly 7.2 ft/s. Capacity scales with the square of the diameter, the square root of the slope, and drops as the pipe material gets rougher — use the calculator above for your exact numbers.
This is a planning-aid capacity estimate based on Manning's equation for uniform, gravity flow. Final culvert sizing should account for inlet control, headwater and tailwater conditions per a site-specific hydraulic study.
How to calculate culvert flow capacity
A culvert's flow capacity depends on how much water can fit through its cross-section (the flow area) and how fast that water can move (governed by slope, roughness and the shape of the wetted cross-section). The standard tool for this is Manning's equation:
For a culvert flowing completely full, the geometry is simple: A = πD²/4 and R = D/4, where D is the inside diameter. When the pipe is only partially full, the wetted area and perimeter come from the geometry of a circular segment, which this calculator solves for any depth from 1% to 100% of the diameter.
Worked example. Take a 24-inch (2 ft) concrete culvert on a 1% slope, flowing full. The flow area is A = π(2)²/4 = 3.14 ft², and the hydraulic radius is R = D/4 = 0.5 ft. With n = 0.013 for concrete and using the US customary form of Manning's equation (Q = 1.486/n · A · R^(2/3) · S^(1/2)): Q = (1.486/0.013) × 3.14 × 0.5^(2/3) × 0.01^(1/2) ≈ 22.6 cfs, which is about 10,150 gallons per minute, at a velocity of roughly 7.2 ft/s.
This is a capacity check, not a full culvert design. Manning's equation describes normal (uniform) flow once water is moving smoothly through the barrel. A culvert's actual performance in a storm is often limited by inlet control — how much water the entrance can accept — which depends on headwater depth and entrance geometry and is evaluated separately per FHWA HDS-5.
Why slope, material and depth change the answer
Slope drives the water downhill; capacity scales with the square root of slope, so doubling the slope only increases capacity by about 41%, not 100%. Roughness (Manning's n) works the opposite way — capacity is inversely proportional to n, so a rough corrugated metal pipe (n ≈ 0.024) carries roughly half the flow of a smooth concrete pipe (n ≈ 0.013) of the same size and slope. Diameter matters most of all, because flow area grows with the square of the diameter while the hydraulic radius (and therefore velocity) also increases — doubling the diameter multiplies full-flow capacity roughly six-fold.
Depth of flow is the least intuitive factor. As a round pipe fills from empty to full, the flow area keeps growing right up to the top — but the wetted perimeter grows a little faster near the top, which slightly shrinks the hydraulic radius. The net effect is that a circular culvert's Manning-equation capacity actually peaks at about 94% of the diameter, just before it runs completely full, and then dips slightly to the 100%-full value. It's a small effect (well under 1%), but it's a genuine quirk of round-pipe hydraulics worth knowing. There's also a tidier fact buried in the same geometry: a culvert flowing exactly half full has precisely half the capacity of the same pipe flowing full, because the hydraulic radius at 50% depth (D/4) is identical to the hydraulic radius when full.
Manning's roughness coefficient by culvert material
The roughness values this calculator uses. Lower n means a smoother interior and higher flow capacity for the same size and slope.
| Material | Manning's n | Relative capacity* |
|---|---|---|
| Smooth HDPE / PVC | 0.010 | 130% |
| Concrete (default) | 0.013 | 100% |
| Corrugated metal, paved invert | 0.019 | 68% |
| Corrugated metal (CMP), unpaved | 0.024 | 54% |
*Relative to concrete, same diameter, slope and depth — capacity is inversely proportional to n. See Manning's n for open channels if you're sizing an unlined ditch instead of a pipe.
Full-flow capacity by diameter
Concrete culvert (n = 0.013) on a 1% slope, flowing completely full. Every value below is exactly what the calculator returns for that diameter.
| Diameter | Flow (cfs) | Flow (gpm) | Velocity (ft/s) |
|---|---|---|---|
| 12 in | 3.56 | 1,599 | 4.54 |
| 15 in | 6.46 | 2,899 | 5.26 |
| 18 in | 10.5 | 4,714 | 5.94 |
| 24 in (common) | 22.6 | 10,153 | 7.20 |
| 30 in | 41.0 | 18,409 | 8.36 |
| 36 in | 66.7 | 29,935 | 9.44 |
| 48 in | 143.6 | 64,468 | 11.4 |
| 60 in | 260.4 | 116,888 | 13.3 |
| 72 in | 423.5 | 190,073 | 15.0 |
Worked examples
24-in concrete driveway culvert, 1% slope, full
22.6 cfs
About 10,150 gpm at 7.2 ft/s. A common size for residential driveway crossings on a gentle grade.
36-in CMP culvert, 0.5% slope, full
25.5 cfs
Corrugated metal's higher roughness (n = 0.024) and the flatter 0.5% slope both hold this larger pipe's capacity close to the smaller concrete example, at 3.6 ft/s.
18-in PVC culvert, 2% slope, ¾ full
17.6 cfs
About 7,900 gpm at 12.4 ft/s. The same pipe flowing completely full would carry 19.3 cfs — partial flow still delivers most of the capacity.
What else affects real-world culvert performance
Inlet control. In many storms, the culvert entrance — not the barrel — limits how much water gets through. A culvert can have plenty of Manning-equation capacity yet still back up water if the inlet is too small, poorly shaped or submerged. FHWA HDS-5 covers inlet-control design in full.
Tailwater and submergence. If the downstream water level rises above the culvert outlet, the pipe can be pushed into pressurized (pipe) flow rather than open-channel flow, and this calculator's normal-depth assumption no longer applies.
Debris and sedimentation. Leaves, gravel and silt reduce the effective flow area and roughen the wetted surface, both of which cut capacity — sometimes drastically. Regular inspection matters as much as the original sizing.
Entrance and outlet geometry. Beveled, tapered or flared end sections improve entrance efficiency and can meaningfully increase a culvert's real-world capacity beyond the plain-barrel Manning estimate used here.
Frequently asked questions
How do you calculate culvert flow capacity?
Culvert capacity is calculated with Manning's equation, Q = (1/n)·A·R^(2/3)·S^(1/2), where A is the flow area, R is the hydraulic radius, S is the slope and n is a roughness coefficient set by the pipe material. For a full circular culvert, A = πD²/4 and R = D/4.
What Manning's n value should I use for a culvert?
Smooth concrete culverts use about n = 0.013. Corrugated metal pipe (CMP) is rougher, around n = 0.024 unpaved or n = 0.019 with a paved invert. Smooth-wall HDPE or PVC culverts are the smoothest common option, around n = 0.010.
Does a culvert flow full or partially full?
Most culverts are designed to flow partially full for most storms, with the full cross-section reserved for rarer, larger events. Manning's equation applies at any depth of flow, not just when the pipe is completely full.
Why does a culvert's flow capacity peak before it's completely full?
In a circular pipe, the wetted perimeter grows faster than the flow area does as the pipe nears the top, which slightly reduces the hydraulic radius. The result is that peak Manning flow occurs at roughly 94% of the diameter, just before the pipe runs completely full.
Does slope or diameter affect culvert capacity more?
Diameter has the larger effect, because flow area grows with the square of the diameter while capacity only grows with the square root of the slope. Doubling the diameter increases full-flow capacity roughly six-fold; doubling the slope increases it by only about 41%.
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.
- Federal Highway Administration. Hydraulic Design of Highway Culverts (HDS-5), FHWA-HIF-12-026.
- American Society of Civil Engineers. Manuals and Reports on Engineering Practice No. 77 — Design and Construction of Urban Stormwater Management Systems.
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)