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Walk-through

How to Use This Calculator

3 steps

1

Enter the flow rate, C factor, diameter, and length

On the Head Loss tab, enter the flow rate in L/s, the Hazen-Williams C factor for your pipe material (check the C Factor Reference tab if you're not sure), the internal diameter in mm, and the pipe length in meters. The calculator updates instantly as you type.

2

Read the head loss and pressure drop

The result card shows the head loss in meters, plus the equivalent pressure drop in kPa and psi. The interpretation line explains what that loss means for the run — a pump or the supply pressure upstream has to overcome it.

3

Or solve for the flow rate a target head loss allows

Switch to the Flow Rate tab, enter a target head loss instead, and the calculator inverts the same equation to tell you the flow rate that produces it — useful when you're working backward from a maximum allowable pressure drop.

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Reference

Formula & Methodology

1 formula

Hazen-Williams equation (SI form)

hf = 10.67 · L · Q^1.852 / (C^1.852 · D^4.87)

hf is the head loss due to friction in meters, L is the pipe length in meters, Q is the flow rate in cubic meters per second, C is the dimensionless Hazen-Williams roughness coefficient, and D is the pipe's internal diameter in meters. The 10.67 constant is the standard SI-unit coefficient for this empirical formula (it differs in the US customary form, which uses 4.73 with Q in ft³/s and D in feet). Solving the same equation for Q gives Q = [hf · C^1.852 · D^4.87 / (10.67 · L)]^(1/1.852), which is how the Flow Rate tab works backward from a target head loss.

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Glossary

Key Terms Explained

7 terms

Hazen-Williams equation An empirical formula, developed in 1906 by Allen Hazen and Gardner Williams, that relates the flow rate of water in a pipe to the friction head loss along its length. It's still the standard method for sizing water distribution and plumbing pipes because it's simpler to apply than the more general Darcy-Weisbach equation.

C factor The Hazen-Williams roughness coefficient — a dimensionless number that captures how smooth or rough a pipe's interior surface is. Higher C means smoother and less friction loss (new PVC is around 150); lower C means rougher and more friction loss (old, corroded cast iron can drop to 80–100).

Roughness coefficient Another name for the C factor. It's an empirical value, not a directly measured physical roughness — it's calibrated so the Hazen-Williams equation matches observed head loss for common pipe materials and ages.

Head loss The reduction in a fluid's pressure, expressed as an equivalent height of fluid column (meters or feet), caused by friction against the pipe wall as it flows. It's the quantity hf solves for directly.

Water pipe Any pressurized pipe carrying water — a supply main, a building's plumbing riser, or an irrigation line. The Hazen-Williams equation applies specifically to water; it's not accurate for other fluids because the C factor was calibrated against water's viscosity.

Friction loss The energy lost to friction as fluid moves through a pipe, expressed here as head loss. It grows with pipe length and with flow rate (roughly to the 1.852 power), and shrinks sharply as diameter increases (to the 4.87 power).

Pressure drop The head loss converted into a pressure unit (kPa or psi) via ΔP = ρ·g·hf, using water's density. It's the same physical loss as head loss, just expressed in pressure terms instead of an equivalent column height — useful for comparing against a pump's rated pressure or a supply main's static pressure.

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Scenarios

Real-World Examples

3 worked examples

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Plumbing designer

100 m run of 100 mm PVC supply pipe

Flow rate 10 L/s C factor 130 Diameter 100 mm Length 100 m

At 10 L/s through a 100 mm pipe over 100 m with C = 130 (a typical cast-iron or mid-life PVC value), the head loss is about 1.90 m — equal to an 18.7 kPa (2.7 psi) pressure drop. Doubling the length would roughly double the loss; increasing the diameter has by far the biggest effect, since D is raised to the 4.87 power.

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Comparing pipe materials

Same run, different C factors

PVC (C = 150) 1.46 m head loss Cast iron (C = 130) 1.90 m head loss Old, corroded pipe (C = 100) 3.09 m head loss

Holding flow rate, diameter, and length constant, swapping from new PVC (C = 150) to an old, corroded pipe (C = 100) more than doubles the head loss — from 1.46 m to 3.09 m. This is why aging distribution systems lose pressure over time even with no change in demand: the pipe's interior roughens and C drops.

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Working backward from a pressure budget

Solving for the flow rate a 1.9 m head-loss budget allows

Target head loss 1.9 m C factor 130 Diameter 100 mm Length 100 m

If a system can only tolerate 1.9 m of head loss over this run, the Flow Rate tab shows that flow rate can be up to about 10.0 L/s (158 GPM) before the loss exceeds budget — the exact inverse of the first example, confirming the two tabs are consistent with each other.

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Deep Dive

Understanding the Hazen-Williams Calculator

3 chapters · 5 min read

The Hazen-Williams equation is the formula civil and plumbing engineers reach for first when sizing a water pipe or checking how much pressure a run will lose to friction. This calculator computes the head loss for a given flow rate, C factor, diameter, and length — or works backward to find the flow rate a target head loss allows.

How the Hazen-Williams Calculator works

The calculator uses the SI form of the Hazen-Williams equation, hf = 10.67 · L · Q^1.852 / (C^1.852 · D^4.87), where hf is the head loss in meters, L is the pipe length in meters, Q is the flow rate in cubic meters per second, C is the roughness coefficient, and D is the internal diameter in meters. The Head Loss tab plugs your inputs directly into this formula. The Flow Rate tab algebraically inverts it — solving for Q given a target hf — so you can work backward from a pressure budget instead of forward from a flow rate.

The equation is empirical: Hazen and Williams calibrated it against real pipe-flow measurements rather than deriving it from first principles, which is why it only applies to water at typical temperatures (roughly 5–25°C) and turbulent flow. For non-water fluids, or for flows that fall outside water's normal viscosity range, the more general Darcy-Weisbach equation is the correct tool.

Inputs and what they mean

Flow rate (Q) is entered in liters per second — a convenient scale for typical residential and commercial supply pipes (roughly 0.5–30 L/s). C factor is the Hazen-Williams roughness coefficient; use the C Factor Reference tab to pick a realistic value for your pipe's material and age rather than guessing. Diameter (D) is the pipe's internal diameter in millimeters — not the nominal size printed on the pipe, which can differ from the true internal bore depending on wall thickness and schedule. Length (L) is the total run length in meters, measured along the pipe (not straight-line distance).

Of these, diameter has by far the largest effect on the result, since it's raised to the 4.87 power — halving the diameter increases head loss by roughly a factor of 29, all else equal. Flow rate and C factor both scale the loss to the 1.852 power, so a 10% increase in flow rate increases loss by about 19%.

Limits and edge cases

The Hazen-Williams equation is only valid for water in turbulent flow through full, closed pipes — it should not be used for other liquids, for gases, for open-channel flow, or for laminar flow at very low velocities. It also loses accuracy outside its calibrated velocity range (roughly 0.3–3 m/s / 1–10 ft/s is typical for water distribution design); for velocities well outside that band, or for non-water fluids, use the Darcy-Weisbach equation instead, which is more general but requires a friction factor from the Moody chart or the Colebrook equation.

The pressure-drop figure this calculator reports assumes standard water density (1000 kg/m³) and standard gravity — it does not account for elevation change along the run, fittings and valve losses (minor losses), or water temperature extremes. For a full system design, add minor losses separately and consult a licensed engineer for anything safety-critical.

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Questions

Frequently Asked Questions

6 questions

What is the Hazen-Williams formula?+

It's an empirical equation, hf = 10.67 · L · Q^1.852 / (C^1.852 · D^4.87) in SI units, that estimates the head loss due to friction in a water pipe from the flow rate, pipe roughness (C factor), diameter, and length. It was developed in 1906 and remains the standard method for sizing water supply and plumbing pipes.

What is the C factor, and how do I pick one?+

The C factor is the Hazen-Williams roughness coefficient — higher means smoother and less friction loss. Use the C Factor Reference tab: new PVC or plastic pipe is around 150, new cast iron around 130, and old, corroded, or heavily scaled cast iron can drop to 80–100. When in doubt, use a lower (rougher) value for a conservative, worst-case estimate.

Does this calculator only work for water?+

Yes. The Hazen-Williams equation's C factor was calibrated specifically for water at typical temperatures and turbulent flow — it isn't accurate for other fluids or for gases. For non-water fluids, use the Darcy-Weisbach equation instead.

How is this different from the Darcy-Weisbach equation?+

Darcy-Weisbach is a more general, physics-derived equation that works for any fluid but requires a friction factor from the Moody chart or the Colebrook equation. Hazen-Williams is an empirical shortcut specific to water that only needs a single roughness coefficient (C), which makes it faster to apply for everyday water-pipe sizing.

What units does the calculator use?+

Flow rate is entered in liters per second (L/s); diameter in millimeters (mm); length in meters (m); the C factor is dimensionless. The result — head loss — is shown in meters, with the equivalent pressure drop in kPa and psi. On the Flow Rate tab, the solved flow rate is also shown in GPM for reference.

Can I solve for the flow rate instead of the head loss?+

Yes — switch to the Flow Rate tab, enter a target head loss along with the C factor, diameter, and length, and the calculator algebraically inverts the Hazen-Williams equation to solve for the flow rate that would produce exactly that head loss.

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Pipe material	Typical C factor
PVC / plastic	150
Copper	130–140
Ductile iron (cement-lined)	140
New steel	140–150
New cast iron	130
Concrete	120–140
Galvanized iron	120
Riveted steel	110
Old / corroded cast iron	80–100

Hazen-Williams Calculator

Pipe & flow

Head loss

Compare scenarios

Target head loss & pipe

Flow rate

Typical C factors by pipe material

How to Use This Calculator

Enter the flow rate, C factor, diameter, and length

Read the head loss and pressure drop

Or solve for the flow rate a target head loss allows

Formula & Methodology

Key Terms Explained

Real-World Examples

Plumbing designer

Comparing pipe materials

Working backward from a pressure budget

Understanding the Hazen-Williams Calculator

How the Hazen-Williams Calculator works

Inputs and what they mean

Limits and edge cases

Frequently Asked Questions

Get a branded PDF of your results

Hazen-Williams Calculator

Pipe & flow

Head loss

Compare scenarios

Target head loss & pipe

Flow rate

Typical C factors by pipe material

How to Use This Calculator

Enter the flow rate, C factor, diameter, and length

Read the head loss and pressure drop

Or solve for the flow rate a target head loss allows

Formula & Methodology

Key Terms Explained

Real-World Examples

Understanding the Hazen-Williams Calculator

How the Hazen-Williams Calculator works

Inputs and what they mean

Limits and edge cases

Frequently Asked Questions

Get a branded PDF of your results

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