Hazen-Williams Equation Calculator
Enter a flow rate, pipe diameter, length, and a C roughness coefficient to get head loss and pressure drop from the Hazen-Williams equation. Pick your pipe material to fill in C automatically, or type your own value. For fluids other than water, use the Darcy-Weisbach pressure drop calculator instead.
Calculate head loss (Hazen-Williams)
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The Hazen-Williams equation
In SI units, with head loss in metres of water, the Hazen-Williams formula for head loss is:
h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.87) - h_f - head loss due to friction (m of water)
- L - pipe length (m)
- Q - volumetric flow rate (m³/s)
- C - Hazen-Williams roughness coefficient (dimensionless)
- D - pipe internal diameter (m)
The equation also appears in a velocity form, which is what the original 1905 work published and what you will find in older textbooks:
V = 0.849 × C × R^0.63 × S^0.54 Here V is velocity in m/s and R is the hydraulic radius, which is D/4 for a full circular pipe. S is the slope of the energy grade line, h_f/L. For a full circular pipe the two forms are algebraically equivalent.
The equation in US customary units
American water and fire protection work usually states it with flow in gallons per minute and diameter in inches:
h_f = 0.002083 × L × (100/C)^1.852 × Q^1.852 / d^4.8655 In this version h_f is in feet of water, L is in feet, Q is in US gpm, and d is in inches. The exponent on diameter is 4.8655 here rather than 4.87. That difference is negligible in practice, but it explains why two textbooks can disagree in the last digit. The calculator above works internally in SI and converts, so you can enter gpm and inches directly.
Hazen-Williams C factors by pipe material
C is not a physical dimension. It is a lumped empirical coefficient, and a higher number means a smoother pipe and less head loss. This is the opposite convention to absolute roughness ε, where a higher number means a rougher pipe.
| Pipe material and condition | C (typical) | C (range) |
|---|---|---|
| PVC, HDPE, plastic | 150 | 140–150 |
| Cement-lined ductile iron | 140 | 130–150 |
| Copper and brass tube | 140 | 130–140 |
| Steel, new welded | 140 | 120–150 |
| Cast iron, new | 130 | 120–140 |
| Galvanized iron | 120 | 100–130 |
| Concrete, average | 120 | 100–140 |
| Cast iron, about 10 years old | 110 | 105–120 |
| Cast iron, about 20 years old | 100 | 89–113 |
| Riveted steel | 100 | 90–110 |
| Cast iron, about 40 years old | 83 | 64–83 |
The aging rows matter more than they look. An unlined cast iron main that starts at C = 130 can sit near C = 100 after twenty years. Head loss scales as C^-1.852, so that drift costs roughly 60% more friction loss at the same flow. Modelling an existing network with new-pipe C values makes the model optimistic, and it surfaces later as unexplained low pressures in the field.
Worked example
A 100 mm cast iron main carries 10 L/s over 100 m. The pipe is new, so C = 130.
Q = 10 L/s = 0.01 m³/s, D = 0.1 m, L = 100 m, C = 130
Q^1.852 = 0.01^1.852 = 1.977 × 10⁻⁴
C^1.852 = 130^1.852 = 8231
D^4.87 = 0.1^4.87 = 1.349 × 10⁻⁵
h_f = 10.67 × 100 × 1.977e-4 / (8231 × 1.349e-5)
h_f = 1.90 m of water ≈ 18.6 kPa ≈ 2.70 psi
For comparison, running the same pipe through Darcy-Weisbach with a friction factor of 0.021 gives about 1.74 m. The 9% gap between the two methods is typical, and it is a fair illustration of how much precision the C factor really carries.
When Hazen-Williams applies, and when it does not
Hazen-Williams is an empirical fit, not a derivation. It was calibrated on water flowing through ordinary pipes at ordinary velocities, and outside those conditions it degrades quietly rather than failing loudly.
It is a reasonable choice when all of these hold:
- The fluid is water, at roughly 15 to 25 °C
- Flow is turbulent, which is nearly always true in a working main
- Velocity is roughly between 0.3 and 3 m/s
- Pipe diameter is 50 mm or larger
- Your code, your utility's standards, or an existing hydraulic model is already built around C factors
Use Darcy-Weisbach instead when:
- The fluid is anything but water — oil, air, steam, glycol, slurry
- Water is hot or near freezing, where viscosity moves far enough to matter
- Flow may be laminar or transitional
- Velocities are very low or very high
- You need the calculation to be defensible from first principles
The underlying reason is that Hazen-Williams has no viscosity term at all. Darcy-Weisbach reaches viscosity through the Reynolds number, which is why it generalises to any fluid. Hazen-Williams bakes water's viscosity into the constant, which is what makes it quick and also what confines it. The full comparison is in Darcy-Weisbach vs Hazen-Williams.
Frequently asked questions
What is the Hazen-Williams equation used for?
Sizing and checking water pipes. It is the standard method in municipal water distribution, fire sprinkler design (NFPA 13 is built on it), and irrigation. Those fields handle almost nothing but water at ambient temperature, and they hold decades of documented C factors for their own pipe stock.
How do I convert a C factor to an absolute roughness?
There is no exact conversion, because C is not a roughness dimension — it absorbs viscosity, velocity, and diameter effects that ε keeps separate. Any equivalence you compute is valid only at the specific diameter and velocity you computed it for. If you need ε for the Moody chart, look it up by material in the pipe roughness calculator rather than converting from C.
Why is the exponent 1.852?
It came out of curve-fitting, not theory. Allen Hazen and Gardner Williams fitted the exponent to experimental head loss data for water in the early 1900s. It lands near 2 because turbulent friction loss varies with roughly the square of velocity. It is not exactly 2, and that gap is what makes the formula empirical rather than derived.
Does Hazen-Williams include minor losses?
No. The formula covers friction along the pipe wall only. Valves, bends, tees, and entries are handled separately, usually by adding an equivalent length of straight pipe to L before running the calculation. Fire protection tables list equivalent lengths directly in feet or metres of pipe for exactly this reason.
Related tools
📉 Darcy-Weisbach Calculator
The general-purpose method, for any fluid and any flow regime.
💧 Head Loss Calculator
Darcy-Weisbach head loss in metres, for pump selection.
⚡ Pipe Flow Velocity Calculator
Check that your velocity sits inside the Hazen-Williams range.
📊 Moody Chart Calculator
Friction factor from Reynolds number and relative roughness.