Hazen-Williams Pipe Flow Calculator
Hazen-Williams pipe flow calculator. Returns friction head loss and velocity in a pressurised water pipe from the C coefficient, diameter, length and flow. Educational.
Hazen-Williams Pipe Flow Calculator
Williams & Hazen (1905): “for ordinary conditions 130 is a fair value for new pipe”; 3rd edition (1920): “130 remains the appropriate value”. EPANET 2.2, Table 3.2: cast iron 130–140.
Small pipes are outside the formula’s fit. Williams & Hazen’s 1920 edition left pipes under 2 inches (50.8 mm) out of its exponent fit because viscosity matters more in them, and warned that in pipes under 1 inch (25.4 mm) flows “may be as much as 10 per cent less” than the formula gives. The result flags both.
Please tick the acknowledgement above before calculating.
How to use the Hazen-Williams calculator
Choose the pipe's C coefficient
C stands for the pipe wall: higher is smoother. Each option shows where its value comes from, and you can enter your own. Published tables give ranges, not single values, so the choice of C moves the answer more than anything else on the form.
Enter diameter, length and flow
Use the internal diameter in millimetres, the pipe run length in metres, and the flow rate in litres per second. Diameter has a huge effect — it's raised to nearly the fifth power.
Acknowledge the disclaimer
Hazen-Williams applies to water in full, pressurised pipes. Tick the acknowledgement to reveal the result.
Read head loss and velocity
You get the friction head loss over the length, the flow velocity, and the loss per 100 m. The page flags a velocity below 0.6 m/s or above 3 m/s, which is a design-practice band rather than a limit of the formula, and separately flags a bore under 2 inches or under 1 inch, where the formula’s own authors warned it fits less well.
Hazen-Williams — a water-pipe formula first used about 1902
An empirical shortcut that stuck
Whenever water flows through a pipe, friction against the wall consumes energy, which shows up as a drop in pressure along the run: the friction head loss. Hazen-Williams is an empirical formula for it, in which one coefficient, C, stands for the pipe wall. Gardner Williams and Allen Hazen printed it in their Hydraulic Tables in 1905, but it is older than the book: their 1920 third edition opens its review of new data with “It is eighteen years since the Williams-Hazen formula was first used and fifteen since the first edition of these tables appeared”. The US EPA’s EPANET 2.2 manual calls it “the most commonly used headloss formula in the US”. In its SI form, head loss equals 10.67 times the length times the flow raised to the power 1.852, divided by C raised to 1.852 and the diameter raised to 4.871. Darcy-Weisbach, the alternative, takes the wall roughness and the water’s viscosity separately; Hazen-Williams folds the wall into C and has no viscosity or temperature term at all.
Two exponents do the heavy lifting. Flow raised to 1.852 means head loss climbs steeply as you push more water through: quadruple the flow and the loss rises about thirteenfold (41.852 = 13.0). Diameter raised to 4.871 means bore is the strongest term in the formula: going from 100 mm to 150 mm at the same flow cuts the head loss to about a seventh (0.139) of what it was.
“…twice as much head is consumed in sending a given volume of water through it as was the case when the pipe was new.”
Williams & Hazen on ageing cast-iron pipe, Hydraulic Tables (1905)Where the C values come from
No single table gives one C per material. The values on this page come from three: Williams & Hazen’s own (1905, revised 1920), Table 3.2 of the EPA’s EPANET 2.2 manual (“Roughness Coefficients for New Pipe”, given as ranges), and Cameron Hydraulic Data, a pump-industry handbook. The default is new cast iron at 130 because that is the one value all three agree on. The 1905 tables also tie the lower values to age: their circled figures give the average age at which cast-iron pipe reaches each C, which for c = 100 is 13 years at 4 inches and 20 years at 42 to 48 inches. Those ages are for soft, clear, unfiltered river water, and the authors called them very rough approximations, not a forecast for any modern pipe. EPANET puts it shortly: “a pipe’s roughness coefficient can change considerably with age.”
Where it applies — and where it doesn't
The formula is for water. EPANET 2.2 says it “cannot be used for liquids other than water and was originally developed for turbulent flow only”. Williams & Hazen wrote that it “was designed primarily for computing the flow of water in pipes” and that it seemed “reasonably well adapted” to open channels too; EPANET notes that the Chezy-Manning formula “is more commonly used for open channel flow”. This calculator handles only full, pressurised circular pipes.
Size is where the authors themselves drew a line. Their 1920 edition left pipes under 2 inches out of its exponent fit, because “viscosity is a greater element in the flow of water in small pipes”, and for pipes under 1 inch it said another formula (Saph and Schoder’s) was better and that, with Williams-Hazen, flows “may be as much as 10 per cent less than would otherwise be expected”. At a fixed flow that is about 1.2 times the head (1/0.9 raised to 1.852 is 1.215, our arithmetic). The result box flags both sizes. The page’s velocity flags, below 0.6 m/s and above 3 m/s, are a separate thing: a design-practice band for water service, not a limit of the formula.
Liou’s 1998 re-analysis of the historic test data in the Journal of Hydraulic Engineering showed that C is not a property of the pipe alone: it varies with Reynolds number and pipe size, so the equation has a narrow range of Reynolds numbers and diameters over which a tabulated C is trustworthy, and the error outside that range is significant. Hazen-Williams also gives only the straight-pipe friction loss; fittings, valves and bends add “minor losses” that are calculated separately. This calculator is educational: use it to see how flow, diameter and C interact, and rely on a qualified engineer and the governing code for any system that must perform.
Diameter to nearly the fifth power, and water only
First used about 1902; the tables were printed in 1905.
SI: h_f = 10.67·L·Q^1.852 / (C^1.852·D^4.871).
The coefficient C bundles pipe roughness.
New cast iron: C = 130 in Williams & Hazen, 130–140 in EPANET 2.2.
Diameter is raised to nearly the fifth power.
Flow raised to 1.852 — loss climbs steeply with flow.
No temperature term: same answer for water at any temperature.
Not for other fluids — use Darcy-Weisbach instead.
Fittings add minor losses on top of pipe friction.
This page flags velocity below 0.6 m/s (settling) and above 3 m/s (noise, hammer, erosion), as design practice, not as limits of the formula.
Frequently asked questions
It is an empirical formula for the friction head loss of water flowing in a pressurised pipe. In SI units, head loss = 10.67 × length × flow^1.852 ÷ (C^1.852 × diameter^4.871), with head loss in metres, length and diameter in metres, and flow in m³/s. The coefficient C captures the pipe's roughness. It's popular because it's simple and tuned for water, avoiding the friction-factor calculation that other methods need.
C is a roughness coefficient: higher means smoother and lower friction. Published tables give ranges. EPANET 2.2’s table for new pipe gives 140–150 for plastic and for steel, 130–140 for cast iron, 120–140 for concrete or concrete-lined pipe and 110 for vitrified clay. Williams & Hazen gave 130 as “a fair value for new pipe” in cast iron and tied lower values to age: in their 1905 tables cast iron reaches 100 in 13 to 20 years, depending on bore, in soft river water. Each option on this page shows its own source, and you can enter your own value.
Because diameter is raised to nearly the fifth power (4.871) in the denominator. At the same flow, going from 100 mm to 150 mm cuts the head loss to about a seventh (0.139) of what it was, and halving the bore multiplies it by about 29 (24.871).
The two differ in what they take in. Darcy-Weisbach uses the wall roughness and the fluid’s own viscosity, so it applies to any liquid and temperature; EPANET 2.2 calls it “the most theoretically correct” and says it “applies over all flow regimes and to all liquids”. Hazen-Williams folds everything into C, and EPANET says it “cannot be used for liquids other than water”. Which one a project uses is set by its engineer and code, not by this page. The pipe flow calculator does Darcy-Weisbach.
No. Hazen-Williams gives only the friction loss along the straight pipe. Bends, valves, tees, reducers, and entries and exits add "minor losses" that must be calculated separately, commonly by converting each fitting into an equivalent length of straight pipe and adding it to the run. In systems with many fittings these minor losses can be significant, so they shouldn't be ignored when sizing for available pressure.
This page uses 0.6 to 3 metres per second as a band for water service and flags anything outside it: below it sediment can settle, above it noise, water hammer and erosion become concerns. It is design practice, not a standard’s requirement and not a limit of the formula; the formula’s own authors drew their line by pipe size, which the page flags separately. Check the velocity against your own design criteria.
Not other liquids: EPANET 2.2 says Hazen-Williams “cannot be used for liquids other than water”. Temperature is subtler. The formula has no temperature or viscosity term, so it gives the same head loss for water at 5 °C and at 60 °C, while real friction falls as water warms and its viscosity drops. Williams & Hazen gave no temperature for the pipe formula; Cameron Hydraulic Data states its basis as water at 60 °F (15.6 °C) and that friction can change by “as much as 40%” between freezing and boiling. For warm or hot water, a method that takes the water’s viscosity, such as Darcy-Weisbach, can show the difference; this one cannot.
Only as accurate as the C value, and C is the weak point. Liou (1998) showed from the original test data that C depends on Reynolds number and pipe diameter as well as on the pipe wall, so a handbook C is reliable only inside the range of flows and sizes it was measured in, and the error outside that range is significant rather than a few per cent. Real pipe roughness also varies and grows with age. In pipes under 1 inch, the authors warned that flows may run up to 10% below the formula. Treat the output as an estimate; a final design is checked by a qualified engineer against the governing code.
Use it for learning and preliminary sizing. A real water system — plumbing, irrigation, fire protection, or mains — must be designed by a qualified engineer to the governing codes and standards, accounting for minor losses, peak demand, pressure requirements, and future pipe condition. Treat the output as an educational estimate, not a final design.
Rounding of the constants. The SI form is derived from the original velocity equation v = 0.849·C·R^0.63·S^0.54, which gives a leading coefficient of 10.674 and a diameter exponent of 4.8704; published versions round these to 10.67 and 4.87, and this page uses 10.67 and 4.871. On a 100 mm pipe the exponent difference moves the head loss by about 0.14%, far less than the spread between published C values. A larger discrepancy almost always means a different C, a different diameter convention (nominal versus internal), or a US-customary form of the equation.
Method & sources
How it computes
Hazen–Williams head loss in SI: h_f = 10.67·L·Q^1.852 / (C^1.852·D^4.871), with h_f and L in metres, Q in m³/s, D the internal diameter in metres and C the wall coefficient (sourced options 150 to 80, default new cast iron 130, or your own); v = Q/(πD²/4), loss per 100 m = 100·h_f/L. Water only, full pressurised pipe, no temperature term. Bores under 2 in and under 1 in are flagged (Williams & Hazen 1920). Straight-pipe friction only; minor losses excluded.
What this tool implements
- SI form of the Williams & Hazen (1905) velocity equation v = 0.849·C·R^0.63·S^0.54; deriving it exactly gives a coefficient of 10.674 and a diameter exponent of 4.8704, which this page rounds to 10.67 and 4.871 (about 0.14 % on a 100 mm pipe). The kernel is tested against EPANET 2.2's published US-unit form (4.727·C^-1.852·d^-4.871·L, ft and cfs), which it matches to 0.03 %.
- Applicability per Liou (1998): C depends on Reynolds number and pipe diameter as well as wall condition, so a tabulated C is trustworthy only inside the flow and size range it was measured in; the error outside that range is significant. Water only (EPANET 2.2 §3). The formula has no temperature term, and Williams & Hazen state no temperature for it. They designed it "primarily" for pipes and found it "reasonably well adapted" to open channels; this page handles full pipes only.
- Small bores are flagged per Williams & Hazen, 3rd ed. (1920): pipes under 2 in were left out of the exponent fit because viscosity matters more there, and under 1 in flows "may be as much as 10 per cent less" than the formula gives, about 1.215 times the head at a given flow.
- Velocity is banded, not limited: below 0.6 m/s flagged low (settling), above 3 m/s flagged high (noise, water hammer, erosion). These are design-practice thresholds, not a standard's requirement and not a limit of the formula.
- Each C option names its source on the page: new plastic 150 and new steel 140 (EPANET 2.2 Table 3.2, 140-150); cement-lined iron or steel 140 (Cameron Hydraulic Data design value); new cast iron 130, the default (Williams & Hazen 1905 and 1920; EPANET 130-140); concrete 120; vitrified clay 110; cast iron at 100 and 80 with the 1905 tables' average ages (13-20 and 26-45 years by bore, soft river water, "very rough approximations"). A custom C can be entered.
- Corrected 2026-10-19: the default C was an unsourced "cement-lined / PVC field 130"; "water near 15 °C" was attributed to Williams & Hazen; the formula was dated to the 1905 book rather than its first use about 1902; going from 100 to 150 mm was said to cut the loss to "roughly a tenth" (it is 0.139); bigger-pipe advice removed.
Sources
- Williams GS, Hazen A. Hydraulic Tables, showing the loss of head due to the friction of water flowing in pipes, aqueducts, sewers, etc. New York: John Wiley & Sons; 1905. https://archive.org/details/hydraulictabless00willrich
- Liou CP. Limitations and proper use of the Hazen-Williams equation. Journal of Hydraulic Engineering 1998;124(9):951-954. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:9(951)
- Lamont PA. Common pipe flow formulas compared with the theory of roughness. Journal AWWA 1981;73(5):274-280. https://doi.org/10.1002/j.1551-8833.1981.tb04704.x
- White FM. Fluid Mechanics. 8th ed. New York: McGraw-Hill Education; 2016. Chapter 6, Viscous flow in ducts — Hazen–Williams as an empirical alternative to Darcy–Weisbach and the limits of its validity.
- Williams GS, Hazen A. Hydraulic Tables. 3rd ed., revised. New York: John Wiley & Sons; 1920. "Additional Data": small-pipe limits, and "eighteen years since the Williams-Hazen formula was first used". https://archive.org/details/hydraulictables03hazegoog
- US Environmental Protection Agency. EPANET 2.2 User Manual, §3 The Network Model, Table 3.2 Roughness Coefficients for New Pipe. https://usepa.github.io/EPANET2.2/3_network_model.html
What can make this go out of date
- None at runtime — the constants are fixed. C is a user choice and must be lowered for aged or scaled pipe.
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