Pipe Water Flow (Hazen-Williams) Calculator
The Hazen-Williams equation is the standard empirical formula for water flow in pressurized pipes, widely used in water supply and irrigation design because it relates flow directly to a single roughness coefficient. This calculator applies its velocity form: the water velocity equals 1.318 times the roughness coefficient times the hydraulic radius raised to the 0.63 power times the energy slope raised to the 0.54 power, in US customary units of feet and seconds. The hydraulic radius for a full round pipe is the diameter divided by four. From the velocity it then computes the volumetric flow by multiplying by the pipe's cross-sectional area, and converts to gallons per minute. Enter the inside diameter in feet, the Hazen-Williams coefficient for the pipe material (around 130 to 150 for plastic and new metal pipe, lower for old rough pipe), and the slope of the energy line in feet of head loss per foot of pipe. The tool returns velocity and flow. The equation applies to water near ordinary room temperature flowing in a full pipe under turbulent conditions. Every figure is computed deterministically from the formula shown below, with a worked example that reconciles exactly to the calculator defaults.
Hazen-Williams velocity is 1.318 x C x R^0.63 x S^0.54. A 0.5 ft pipe with C of 130 and a 0.01 slope flows at about 3.85 ft/s, roughly 338.86 gallons per minute.
Hazen-Williams flow formula
V = 1.318 x C x R^0.63 x S^0.54
R = hydraulic radius = D / 4 (ft)
C = Hazen-Williams roughness coefficient
S = energy slope (ft of head loss per ft)
Q (gpm) = V x area x 448.831
The 1.318 constant applies to US units of feet and seconds. For a full round pipe the hydraulic radius is the diameter over four. The result converts cubic feet per second to gallons per minute with the 448.831 factor.
Worked example
Suppose the pipe inside diameter is 0.5 feet (6 inches), the Hazen-Williams C is 130, and the energy slope is 0.01 feet per foot.
- Hydraulic radius: 0.5 / 4 = 0.125 ft
- R^0.63 = 0.125^0.63 = 0.2698
- S^0.54 = 0.01^0.54 = 0.08316
- Velocity: 1.318 x 130 x 0.2698 x 0.08316 = 3.85 ft/s
- Area: pi/4 x 0.5^2 = 0.19635 sq ft; Q = 3.85 x 0.19635 x 448.831 = 338.86 gpm
The flow velocity is about 3.85 feet per second, a flow of roughly 338.86 gallons per minute. These are the calculator's default inputs, so the result matches the widget exactly.
Pipe Water Flow (Hazen-Williams) Calculator: frequently asked questions
What is the Hazen-Williams equation?
It is an empirical formula for the velocity or flow of water in a pressurized pipe, relating flow to pipe diameter, a roughness coefficient and the slope of the energy grade line. It is popular in water-supply and sprinkler design because it uses one material coefficient and applies well to typical water temperatures.
What is the C coefficient?
C is the Hazen-Williams roughness coefficient for the pipe material and condition. Smooth materials such as plastic and new copper have high values around 140 to 150, while old, rough or corroded pipe has lower values. A higher C means less friction and more flow for the same slope.
What is the energy slope?
The energy slope, S, is the head loss per unit length of pipe, expressed as feet of head lost per foot of pipe. It represents the driving gradient for flow. A steeper slope, from greater pressure difference or elevation drop over the length, produces higher velocity and flow.
When is Hazen-Williams not appropriate?
It is calibrated for water at ordinary temperatures in turbulent flow and full pipes. For other fluids, very cold or hot water, very small pipes, or laminar flow, the Darcy-Weisbach equation is more general and accurate. Use Hazen-Williams within its intended water-supply range.
How do I convert flow units?
This calculator computes velocity in feet per second and flow in gallons per minute. Cubic feet per second times 448.831 gives gallons per minute. Keep diameter and slope in the units the formula expects, feet and feet per foot, to get correct results. The Department of Energy publishes water-system efficiency guidance.
Official sources
- Water systems and pumping efficiency guidance: US Department of Energy (DOE). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.