Culvert Pipe Volume Calculator
Find the water volume of a round culvert or pipe — full or at any fill depth — in cubic feet, gallons and water weight, plus its Manning flow capacity from the slope and pipe material, with a depth-by-depth table and common culvert sizes.
How it works
full volume = π × (D ÷ 2)² × length · partly full area = (r² ÷ 2)(θ − sin θ), θ = 2·acos((r − h) ÷ r) · gallons = cu ft × 7.48 · water weight = cu ft × 62.4 lb · Manning flow Q = (1.486 ÷ n) × A × R^(2/3) × √S (US) or (1 ÷ n) × A × R^(2/3) × √S (SI), R = area ÷ wetted perimeter (D ÷ 4 when full)
A full pipe is a cylinder: π r² times its length, with everything in the same unit. When it runs partly full the water fills a circular segment, whose area follows from the water depth h through the angle θ = 2·acos((r − h) ÷ r); multiplying by the length gives the volume, ×7.48 converts cubic feet to US gallons and ×62.4 gives the weight of fresh water in pounds. For flow, the calculator uses Manning’s equation for uniform flow: the area times the hydraulic radius (area ÷ wetted perimeter) to the 2/3 power, times the square root of the slope, divided by the roughness n of the pipe wall — about 0.012–0.013 for concrete or smooth-lined plastic and 0.022–0.024 for corrugated pipe. A round pipe actually carries the most at about 94% depth, slightly more than when completely full, because the last few percent of area add more wetted wall than flow. These are barrel capacities: a real road culvert is often limited by its inlet and by how high the water may back up upstream, so drainage standards size crossings with inlet-control charts.
Worked example
An 18 in culvert 40 ft long: radius 0.75 ft, area π × 0.75² = 1.767 sq ft, full volume 1.767 × 40 = 70.7 cu ft = 529 gallons, which weighs about 4,410 lb. At 50% depth the segment area is half of that, about 35.3 cu ft. Laid at a 1% slope in concrete (n 0.013), it carries about 10.5 cfs (4,715 gpm) running full at 5.9 ft/s.
Sources: FHWA — Hydraulic Design of Highway Culverts, HDS-5 (FHWA-HIF-12-026) · Engineering ToolBox — Volume in partly filled horizontal pipes
Frequently asked questions
Does this give the culvert’s flow capacity?
Yes — turn on the flow estimate and enter the slope and pipe material. It gives the Manning (uniform-flow) capacity of the barrel, full and at your depth. That is the most the pipe itself can carry; at a road crossing the inlet shape and the allowable headwater often limit the flow first, so a drainage engineer or your county standard should confirm the size.
What size culvert do I need for a driveway?
It depends on the area that drains to the ditch and the design storm. 15–18 in is a common minimum for a residential driveway, but ditches with more runoff need larger. Many counties set a minimum size and require a permit. The common-sizes table shows how much each size carries at your slope.
How do I convert cubic feet to gallons?
Multiply cubic feet by 7.48 to get US gallons (there are 7.48052 gallons in a cubic foot). For litres, multiply cubic feet by 28.317, and for cubic metres divide by 35.31.
Why does a pipe carry more water at 94% depth than full?
Flow depends on area and on the hydraulic radius (area ÷ wetted wall). Near the top the water gains little extra area but touches a lot of extra wall, which adds friction, so the peak flow of a round pipe is at about 93.8% depth — roughly 7% more than when completely full.
What Manning n should I use?
Concrete about 0.013, smooth-lined HDPE or PVC about 0.012, and corrugated metal or single-wall corrugated plastic about 0.022–0.024. Older, dented or partly silted pipes run rougher, so a higher n gives a more cautious capacity.
Related calculators
Estimates only — add for waste and confirm against local building codes and supplier specs.