What is the Hazen-Williams formula?

The Hazen-Williams equation is V = k · C · R^0.63 · S^0.54, where V is flow velocity, C is the roughness coefficient, R is the hydraulic radius (D/4 for a full circular pipe), S is the hydraulic gradient (head loss / pipe length), and k is a unit constant (0.8492 in SI, 1.318 in US customary units).

What does the C coefficient represent?

C is the Hazen-Williams roughness coefficient. Higher C means a smoother pipe with less friction: new PVC or smooth plastic is around 150, new cast iron around 130, galvanized steel around 120, and old/corroded cast iron can drop to 80 or below.

What is the hydraulic gradient S?

S is the head loss divided by the pipe length — a dimensionless ratio. For example, a pipe that loses 2 m of head over 400 m has S = 2/400 = 0.005. Typical water mains operate in the range 0.001 to 0.01.

Is the Hazen-Williams formula accurate for all fluids?

No — it is calibrated for water at typical service temperatures (near 60 °F / 15 °C). It should not be used for gases, oils, or water at extreme temperatures. For other fluids, use the Darcy-Weisbach equation with the appropriate viscosity.

What is a reasonable pipe velocity for water?

General guidance: 0.6–1.5 m/s (2–5 ft/s) for domestic supply, up to 3 m/s (10 ft/s) for short fire-flow lines. Velocities above 3 m/s risk water hammer and accelerated erosion.

Hazen-Williams Calculator

Name: Hazen-Williams Calculator
Availability: InStock
Author: Nham Vu

Enter pipe diameter, hydraulic gradient, and Hazen-Williams C coefficient to instantly compute water flow velocity and volumetric flow rate.

Unit System

Pipe Diameter

Internal diameter (mm)

Common:

Hydraulic Gradient (S)

Head loss / pipe length (dimensionless)

Example: 5 m loss over 1000 m → S = 0.005

Hazen-Williams C Coefficient

C value (custom)

Fill in the inputs and click Calculate.

Flow Velocity

—

Flow Rate (Q)

—

Velocity Assessment

0 m/s Typical: 0.6–1.5 m/s 3+ m/s

Formula Breakdown

V = k · C · (D/4)^0.63 · S^0.54

Results Summary

Parameter	Metric	Imperial

Summary

Enter pipe diameter, hydraulic gradient, and Hazen-Williams C coefficient to instantly compute water flow velocity and volumetric flow rate.

How it works

Enter the internal pipe diameter in millimeters or inches.
Enter the hydraulic gradient S (head loss per unit length, dimensionless — e.g. 0.005 for 5 m loss per 1000 m).
Select or enter the Hazen-Williams C coefficient for your pipe material.
Click Calculate to get velocity and flow rate in both SI and Imperial units.
Switch between metric and Imperial unit systems using the toggle at the top.

Use cases

Size water supply pipes for residential or commercial buildings.
Estimate fire-flow capacity in a municipal distribution network.
Check whether an existing pipe can deliver the required flow rate.
Compare C values for different pipe materials to select the best option.
Solve hydraulics and civil engineering homework problems step by step.
Verify pump sizing by confirming expected pipe velocity and flow.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu