Culvert size for a driveway or farm crossing

What the number means

The big number is the smallest inside diameter at which a pipe running full, on the slope you gave, carries the design flow. A pipe is never bought at that exact size, so round up to the next one available, and then check the headwater, the outlet and the cover over the pipe.

How do I size a culvert pipe?

Find the peak flow the pipe must pass, then pick a diameter that carries it. For a small drainage area the Rational Method gives the flow, Q = C × i × A. Manning's equation then gives the capacity of the pipe running full. The smallest diameter whose capacity reaches the flow is the minimum, and you round up to the next available size.

What is the Rational Method?

Peak flow in cubic feet per second = C × i × A, where C is a runoff coefficient from 0 to 1, i is the rainfall intensity in inches per hour and A is the drainage area in acres. The FHWA culvert manual says it is best applied to drainage areas smaller than 200 acres. Strictly the answer is 1.008 times larger, a unit conversion that everyone leaves out.

What Manning n do I use?

HDS 5 gives typical design values of 0.012 for smooth-walled culverts such as concrete and 0.024 for corrugated metal. Its table of laboratory values lists 0.010 to 0.011 for concrete pipe, 0.018 to 0.025 for corrugated polyethylene and a wide span for corrugated metal depending on the corrugation size, and it warns that field values are higher because of joints, abrasion, corrosion and deflection. Type your own n in the optional field if you have a manufacturer's value.

What is HW/D?

The headwater depth, the depth of ponded water at the inlet, divided by the pipe height. Agencies limit it so that water does not flood the road or the yard. HDS 5 says the allowable ratio commonly ranges from 1.0 to 1.5. This calculator does not find the headwater.

What rainfall intensity should I use?

The intensity for the storm your local rules specify, such as a 10-year or 25-year return period, at a duration equal to the time the water takes to travel from the farthest point of the drainage area to the pipe (the time of concentration). You can read it from NOAA Atlas 14 for a US site. A short, steep, paved area has a short time and a high intensity.

What runoff coefficient C should I use?

It depends on the surface, the slope and the soil, and the values come from your local drainage manual; we do not tabulate them. Roughly, paved or roofed ground sends most of the rain to the pipe and C is high, while level woods or lawn on sandy soil sends little. Take the area-weighted average for a mixed catchment.

Does this work for a driveway or road crossing?

It gives a first estimate for the pipe itself. A crossing also needs the right headwater, an inlet and outlet that do not erode, a cover over the pipe that carries the load, and often a permit. Anything on a public road needs an engineered design.

Full-pipe capacity with Manning's equation

For a circular pipe flowing full, area is π D² ÷ 4 and hydraulic radius is D ÷ 4, so velocity is V = (1.486 ÷ n) × R^(2/3) × S^(1/2) with D in feet and S the slope as a fraction (FHWA HDS 5, equation B.3), and flow is Q = V × area. Solving for the diameter gives D = [Q × n ÷ (0.4632 × √S)]^(3/8) in feet. The capacity rises steeply with diameter, as D^(8/3): doubling the diameter multiplies it by about 6.3. That is why a pipe one size up has much more margin.

Worked example

A 2-acre field with C = 0.5 in a rain of 4 in/h sends Q = 0.5 × 4 × 2 = 4.0 cfs. At a 2 percent slope a corrugated metal pipe (n = 0.024) needs at least 13.8 inches, so you would choose the next size up; an 18 inch pipe then carries 8.0 cfs full at 4.6 ft/s. A smooth-wall pipe (n = 0.012) at the same slope needs only 10.7 inches. Roughness matters: a 12 inch smooth pipe at 1 percent carries 3.86 cfs with n = 0.012 and 3.56 cfs with n = 0.013.

Limits of this method

Full-pipe Manning flow is the capacity of the barrel when the outlet is free, not the capacity of the culvert. HDS 5 explains that a culvert may be controlled at its inlet, where the entrance shape and the headwater decide the flow, or at its outlet, where the barrel and the tailwater decide; you work out the headwater for both and the higher of the two controls (HDS 5, section 3.3.5), and it has to stay inside the allowed HW/D. A trash rack, a debris plug or an ice-blocked inlet cuts the flow further. The Rational Method also assumes steady rain over the whole area for a time equal to the time of concentration, which is a rough picture of a real storm.

Common mistakes

Using the nominal diameter of a corrugated pipe when the inside diameter is smaller. Using a smooth-wall n for a corrugated pipe, which overstates capacity by about twice. Using a yearly rainfall number in place of an hourly intensity. Skipping the outlet: a pipe that carries the water but ends in bare soil erodes a gully. Putting the pipe at a slope different from the ditch, so the real slope is not the one you typed.

Sources: Federal Highway Administration, Hydraulic Design of Highway Culverts (HDS 5), third edition, FHWA-HIF-12-026, April 2012: section 2.2 (Rational Method, areas under 200 acres), the headwater-ratio discussion (HW/D commonly 1.0 to 1.5), the outlet-control discussion (n of 0.012 and 0.024) and appendix B, equation B.3 and table B.1 (Manning’s n for culverts); NOAA Atlas 14. The runoff coefficient is not tabulated here. Related: pipe slope calculator, French drain calculator, swale capacity calculator, gravel calculator. How we check our calculators.