Hazen Williams Equation Calculator

Hazen Williams Equation Calculator finds friction head loss, pressure drop, flow rate, or the smallest bore for water in a full pipe, using NFPA 13 C-factors and Schedule 40 sizes.

Using the Hazen Williams Equation Calculator

The Hazen Williams Equation Calculator works in four directions. Pick Solve For first, then fill only the boxes that stay visible. Head loss mode needs flow, inside diameter, length and C, while flow mode and diameter mode swap one of those for the head loss you can accept.

The fourth mode works backward from a field flow test. Enter the measured flow and the measured friction drop over a known run, and the tool returns the C-factor that pipe actually has today. Use that number in place of a book value when an old main or sprinkler riser no longer behaves like new pipe.

Enter the inside diameter, not the nominal size. A 4 in Schedule 40 pipe has a 4.026 in bore, and the arrow beside the box fills Schedule 40 bores from 1/2 in through 12 in. Diameter sits under an exponent near 4.87, so typing 4 instead of 4.026 already shifts the loss by about 3 percent.

The closed panel under the main inputs holds fittings, minor losses, elevation and inlet pressure. Fittings go in as equivalent feet of pipe, either sized for your pipe's C or read straight off the NFPA chart. Valves and fittings you only know by K value go in the Minor Loss K Total box instead.

A positive elevation means the outlet sits higher than the inlet, and a negative one means it drops. Adding an inlet pressure unlocks the outlet pressure result. The Units box switches between US Customary and SI metric and converts your entries in place.

Hazen-Williams Formula for Pipe Flow

The equation was fitted to test data for water, so its constant depends on the units you feed it. The SI form takes flow in m³/s, diameter and length in meters, and returns head loss in meters of water.

$$h_f=\frac{10.67\cdot L\cdot Q^{1.852}}{C^{1.852}\cdot d^{4.8704}}$$

Here h_f is friction head loss, L is pipe length, Q is flow, C is the roughness coefficient and d is the inside diameter. Converting the same equation to gpm, inches and feet gives the US form that the Hazen Williams Equation Calculator uses by default.

$$h_f=\frac{10.44\cdot L\cdot Q^{1.852}}{C^{1.852}\cdot d^{4.8704}}$$

An older US version writes the constant as 0.002083 with a (100/C) term and a 4.8655 exponent on d. The EPANET 2.2 user manual lists a third version with flow in cfs and diameter in feet, using 4.727 and an exponent of 4.871. All of them describe the same physics with slightly different rounding.

NFPA 13 pressure form

Fire sprinkler work uses a form that returns pressure loss per foot of pipe instead of feet of head. Q stays in gpm and d in inches, and both exponents are rounded.

$$p=\frac{4.52\cdot Q^{1.85}}{C^{1.85}\cdot d^{4.87}}$$

The 4.52 constant gives psi per foot, not feet of head. Some references label this version as head loss, which understates the loss by a factor of 2.31 if the answer is read as feet. Pick the NFPA 13 option under Formula Constants when your numbers must match a sprinkler hydraulic sheet.

Velocity form

The original Hazen-Williams form gives mean velocity from the hydraulic radius R and the friction slope S. For a round pipe flowing full, R equals d/4.

$$V=1.318\cdot C\cdot R^{0.63}\cdot S^{0.54}$$

This version takes R in feet and returns velocity in ft/s. In SI units the constant becomes 0.849 with R in meters and V in m/s. Multiplying V by the flow area gives Q, which is how the head loss form above was derived.

Solving for flow or diameter

Rearranging the SI head loss form gives the flow and diameter equations behind the other two modes. The same rearrangement works with the US constant.

$$Q={\left(\frac{h_f\cdot C^{1.852}\cdot d^{4.8704}}{10.67\cdot L}\right)}^{1/1.852}$$

$$d={\left(\frac{10.67\cdot L\cdot Q^{1.852}}{C^{1.852}\cdot h_f}\right)}^{1/4.8704}$$

The diameter exponent is why bore matters most. At 250 gpm over 500 ft of C 120 pipe, dropping from 4 in to 3 in Schedule 40 raises the loss from 23.0 ft to 86.5 ft. Stepping up to 6 in cuts it to 3.1 ft.

Worked Example at 250 gpm

The Hazen Williams Equation Calculator opens on a common case. Water flows at 250 gpm through 500 ft of 4 in Schedule 40 black steel in a wet system, which NFPA 13 rates at C 120. The bore is 4.026 in, the outlet sits 10 ft above the inlet, and the inlet runs at 65 psi.

$$h_f=\frac{10.44\cdot 500\cdot 250^{1.852}}{120^{1.852}\cdot 4.026^{4.8704}}=23.02\text{ft}$$

That 23.02 ft of head equals 9.98 psi of friction drop. Water moves at 6.30 ft/s through a 12.73 in² flow area. Lifting it 10 ft costs another 4.33 psi, so the outlet sees 65 minus 9.98 minus 4.33, or 50.69 psi.

Running the same case through each published constant set shows why online calculators rarely agree to the last decimal. The spread comes from rounding in the constants, not from an error in any one of them.

Formula Form	Constants	Head Loss	Pressure Drop
Standard US	10.44, 1.852, 4.8704	23.02 ft	9.98 psi
Older US	0.002083, 1.85, 4.8655	23.14 ft	10.03 psi
NFPA 13	4.52, 1.85, 4.87	22.97 ft	9.96 psi

What Each Result Card Shows

The large box in the Hazen Williams Equation Calculator shows the value you solved for, with a second unit underneath. The four cards around it answer the next question a designer usually asks, and the fourth card changes content with the solve mode.

Friction slope and psi per foot

Friction slope is the loss per 100 ft of pipe, 4.60 ft/100 ft in the example. The card also gives 0.0200 psi per foot, the rate a sprinkler hydraulic sheet lists for each segment. Multiply either rate by a new length to scale the loss without running the tool again.

Flow velocity and velocity head

Velocity is flow divided by bore area. Velocity head, V²/2g, is 0.617 ft in the example, and multiplying it by a fitting's K value gives that fitting's loss in feet. The EPANET manual lists K at 0.2 for an open gate valve, 2.5 for an open swing check and 1.8 for flow through a tee branch.

Add the K values for every fitting in the run and type the sum into Minor Loss K Total. The tool multiplies it by the velocity head and carries that loss into the outlet pressure. A K total of 5 on the example adds 1.34 psi and lowers the outlet from 50.69 psi to 49.35 psi.

The card turns amber once velocity passes 8 ft/s (2.4 m/s). That limit follows the Copper Development Association piping design guide, which keeps cold water at 5 to 8 ft/s to control erosion, noise and surge.

Outlet pressure

This card takes the inlet pressure and subtracts pipe friction, any minor loss from the K box and the pressure needed to lift water to the outlet. It turns red with a Short at Outlet label when the run needs more than the inlet supplies. Leave the inlet box blank and the card switches to total pressure loss instead.

Darcy factor, Manning n and power

The fourth card restates the same loss as a Darcy friction factor, 0.0250 here, and an equivalent Manning n of 0.0097. Those let you cross-check a Darcy-Weisbach or Manning result for the same pipe. Water power lost, 1.45 hp in the example, is the pumping power friction burns before any pump or motor losses.

In diameter mode this card names the smallest Schedule 40 size whose bore meets the minimum, with the loss and velocity you get in it. Past 12 in, it counts how many parallel 12 in lines would carry the flow. In C-factor mode it shows how much of C 150 capacity the tested pipe still has.

Grade line, size table and Excel formula

The Hydraulic Grade Line panel draws pressure head along the run, scaled to the pipe's rise or drop. The size table reruns your case for the Schedule 40 sizes on either side of yours. The math panel prints every substitution plus a spreadsheet formula you can copy.

C Factor by Pipe Material

C is a smoothness rating, so a higher number means less friction. Because C sits under a 1.852 power, the drop from 120 to 100 raises the example loss from 23.0 ft to 32.3 ft. A wrong C moves the answer more than most people expect.

Pipe Material	NFPA 13 C	Other Published Values
PVC, CPVC (listed plastic)	150	PVC 150 design (Uni-Bell)
Polyethylene, HDPE	Not listed	140 (Toro HD Poly chart), plastic 140 to 150 new (EPANET)
Copper, brass, stainless	150	Copper and brass 130 design (Toro)
Cement-lined cast or ductile iron	140	Concrete lined 120 to 140 new (EPANET)
Asbestos cement	140	140 design (Toro)
Concrete	140	120 to 140 new (EPANET)
Black or galvanized steel, wet	120	Galvanized iron 120 new (EPANET)
Black or galvanized steel, dry	100	Welded steel 100 design (Toro)
Unlined cast or ductile iron	100	Cast iron 130 to 140 new (EPANET), 100 design (Toro)

The NFPA 13 column is fixed by the NFPA 13 sprinkler standard, and those values fill the material dropdown of the Hazen Williams Equation Calculator. The dropdown also offers C 140 for polyethylene, the value Toro's HD Poly friction loss chart is built on. Water supply and irrigation designers choose C for pipe age and condition instead, which is why new-pipe and design values differ in the Toro irrigation C table.

Plastic holds its value over time. The PVC pipe industry's Uni-Bell hydraulic testing found new and 1976-installed PVC still above C 150, so 150 is a conservative design figure. Metal pipe is different, since corrosion and tuberculation raise roughness with age, and a C-Factor mode run on a flow test beats a guess for an old cast iron main.

Fittings and Equivalent Length

Hazen-Williams covers straight pipe only. Elbows, tees and valves add loss that the tool takes as extra feet of pipe in the Fittings Equivalent Length box. NFPA 13 publishes these lengths for Schedule 40 steel at C 120, where a 4 in standard 90° elbow counts as 10 ft, a branch tee as 20 ft and an open gate valve as 2 ft.

Those chart lengths only hold at C 120. NFPA 13 scales them by (C/120)^1.85 for other pipe. Smooth pipe needs a longer run to lose the same pressure as the fitting, so the multiplier climbs above 1 as C rises.

Pipe C Value	Multiplier	4 in Standard Elbow
100	0.713	7.1 ft
120	1.00	10 ft
130	1.16	11.6 ft
140	1.33	13.3 ft
150	1.51	15.1 ft

You don't have to apply the factor by hand. Set Fittings Length Basis to NFPA chart (C 120 basis), type the chart total, and the Hazen Williams Equation Calculator scales it to your pipe's C. Leave it on Lengths for my pipe C when your equivalent lengths already match the pipe.

In the example, two standard elbows, one branch tee and a gate valve add 42 ft at C 120, raising the loss from 23.02 ft to about 24.96 ft. On C 150 pipe, 500 ft of 4 in pipe plus 50 ft of chart fittings counts as 575.6 ft and loses 17.53 ft of head.

Head Loss to Pressure Drop

Head loss and pressure drop describe the same lost energy in different units. A one-foot column of water near room temperature presses down with 0.433 psi, so one psi holds up 2.31 ft of water. The Hazen Williams Equation Calculator uses 62.4 lb/ft³ for these conversions.

$$\Delta P=0.433\cdot h_f$$

In SI units, one meter of water equals about 9.81 kPa, or 1.42 psi. The table covers the head and pressure pairs people look up most. For pump total head and discharge pressure, the Pump Pressure Calculator handles the conversion in both directions.

Water Column	Pressure
1 ft	0.433 psi
1 m (3.28 ft)	1.42 psi (9.81 kPa)
2.31 ft	1 psi
20 ft	8.67 psi
92.3 ft	40 psi
300 ft	130 psi
692 ft	300 psi
1,000 ft	433 psi

Height costs pressure the same way friction does. A faucet 20 ft above the meter needs 8.67 psi just for the lift, so getting 40 psi at that faucet takes 48.7 psi at the meter before any friction loss is added.

Sizing Pipe From Allowable Loss

Diameter mode in the Hazen Williams Equation Calculator finds the smallest bore that keeps the loss within your budget. That bore is rarely a stock size, so the result card rounds up to the next Schedule 40 pipe. The table lists the sizes the tool uses, with inside diameter equal to outside diameter minus twice the wall.

Nominal Size	OD (in)	Wall (in)	Sch 40 ID (in)
1/2	0.840	0.109	0.622
3/4	1.050	0.113	0.824
1	1.315	0.133	1.049
1-1/4	1.660	0.140	1.380
1-1/2	1.900	0.145	1.610
2	2.375	0.154	2.067
2-1/2	2.875	0.203	2.469
3	3.500	0.216	3.068
4	4.500	0.237	4.026
5	5.563	0.258	5.047
6	6.625	0.280	6.065
8	8.625	0.322	7.981
10	10.750	0.365	10.020
12	12.750	0.406	11.938

Nominal size only matches the OD from 14 in up, which is why a 12 in pipe measures 12.750 in outside and 11.938 in inside. No standard pipe has a 1.000 in OD. The closest is 3/4 in nominal at 1.050 in, so a tape reading near 1 in usually means 3/4 in pipe.

Check velocity before accepting a size. Fast flow adds noise, erosion and surge risk on top of friction, so the tool warns once velocity passes 8 ft/s. At 250 gpm, 2 in pipe runs near 24 ft/s and triggers that warning, while 4 in holds a comfortable 6.3 ft/s. To estimate how much water a chosen line holds, the Pipe Volume Calculator uses the same bore.

Hazen-Williams vs Manning vs Darcy

All three methods predict friction loss, but each suits a different job. The EPANET manual notes that Hazen-Williams can't be used for liquids other than water and was built for turbulent flow. Darcy-Weisbach covers every liquid and flow regime, and Manning is more common for open channels. The Hazen Williams Equation Calculator also reports the Darcy f and Manning n that match its result, so one pipe can be compared across all three.

Method	Best Fit	Roughness Term
Hazen-Williams	Water in full, pressurized pipe	C, higher is smoother
Darcy-Weisbach	Any liquid, hot water, small tubing	f, from Reynolds number and roughness
Manning	Gravity flow, channels, sewers, culverts	n, higher is rougher

Manning's formula for a pipe flowing full uses hydraulic radius R = d/4. In US units Q is in cfs, the flow area A is in ft², R is in feet and S is the pipe slope as a decimal.

$$Q=\frac{1.486}{n}\cdot A\cdot R^{2/3}\cdot S^{1/2}$$

A sewer or storm line running partly full needs the Manning's Flow Calculator or the Partial Pipe Flow Calculator instead. Road and driveway crossings have their own inlet and outlet checks in the Culvert Flow Calculator.

Hazen Williams Calculator in Excel

The math panel of the Hazen Williams Equation Calculator prints an Excel or Google Sheets formula built from your own entries. Copy it into a cell to keep the calculation inside a pipe schedule. For the worked example, the US head loss version reads as below.

=10.4422*500*250^1.852/(120^1.852*4.026^4.8704)

To reuse it, put flow in gpm in A2, inside diameter in inches in B2, length in feet in C2 and C in D2. The formula below then returns head loss in feet, and multiplying the result by 0.433 converts it to psi.

=10.44*C2*A2^1.852/(D2^1.852*B2^4.8704)

For the Hazen-Williams equation in SI units, swap 10.44 for 10.67 and enter Q in m³/s with d and L in meters. With flow in L/s and bore in mm, divide both by 1,000 inside the formula. A diameter left in millimeters is the most common metric spreadsheet mistake, and it shows up as an absurdly small loss.

Flow, Head and Pressure Basics

These answers cover the questions that come up most often around the Hazen Williams Equation Calculator, from flow and head to psi conversions. Each one uses the same water properties as the tool.

What is the Hazen-Williams equation used for?

It estimates friction loss for water in full, pressurized pipe. Water utilities use it to size mains, irrigation designers use it for laterals, and sprinkler designers use it in NFPA 13 hydraulic calculations. It is popular because C stays roughly constant for a pipe material, so no Reynolds number lookup is needed.

Its main job is answering whether a pipe can deliver enough flow at enough pressure. A sprinkler system or hydrant has to meet a demand at a residual pressure, and the Fire Flow Calculator sets that demand before this tool checks the piping.

How do I calculate water flow?

Flow equals velocity times flow area, Q = V × A. A 4 in Schedule 40 bore has 0.0884 ft² of area, so water at 6.30 ft/s moves 0.557 cfs. One cfs equals 448.8 gpm, which brings that flow to 250 gpm.

When you know the pressure budget instead of the velocity, switch the tool to flow mode and enter the allowable head loss. For a measured flow, time how long a container takes to fill and run the numbers in the Gallons Per Minute Calculator or, in metric, the Liters per Minute Calculator. The Pipe Flow Calculator handles the velocity times area case directly.

How do I calculate head loss in a pipe?

Measure the inside diameter, the total length and the flow, then pick a C for the material. Add fitting equivalent lengths to the straight length, adjusted for C. Run the head loss form and convert the feet of head to psi with 0.433 if you need pressure.

Head loss is energy, not water. No water leaves the pipe; friction against the wall turns some pressure into heat. Elevation change is a separate term, which is why the tool keeps the lift pressure on its own row instead of folding it into friction.

How do I calculate my water pressure?

The direct way is a gauge on an outside hose bib with every fixture closed, which reads static pressure. Open a faucet and read it again to see working pressure under flow. The gap between the two readings is the friction and meter loss at that flow.

For a gravity supply, multiply the height of the water surface above the outlet by 0.433. A tank surface 92.3 ft above a tap gives 40 psi at that tap with no flow, and anything less once friction starts.

What C value should I use for PVC or HDPE?

Use 150 for PVC pressure pipe. The PVC pipe industry recommends it as a conservative design value, and its lab and field tests on new and decades-old pipe came in higher. NFPA 13 also assigns 150 to listed plastic sprinkler pipe such as CPVC.

For polyethylene and HDPE, published design values sit at 140 to 150. Toro builds its HD Poly friction loss chart on C 140, while EPANET lists new plastic pipe at 140 to 150. The tool's polyethylene option uses 140, and you can type 150 for new, clean pipe.

What is Hazen's formula?

Hazen's formula without Williams is a separate soil relation from Allen Hazen's filter sand work. It estimates the permeability of clean sand from its effective grain size, D10, with permeability rising with the square of that size. Some texts call it the Hazen method.

It has nothing to do with pipe friction, so it can't replace the Hazen-Williams equation for pipes. For how fast water soaks into ground on site, field percolation data in the Soil Infiltration Rate Calculator gives a more direct answer.

What is 1 psi equal to?

PSI stands for pounds per square inch. One psi equals 2.31 ft of water, 0.703 m of water and 6.895 kPa. In the kilogram-force units still used on many gauges, 1 psi is 0.0703 kgf/cm², and 1 kgf/cm² is 14.22 psi.

To convert psi to kgf/cm², multiply by 0.0703. A 40 psi reading is 2.81 kgf/cm², and 300 psi is 21.1 kgf/cm². One bar is 14.50 psi, which equals 33.5 ft of water.