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Hazen–Williams Calculator — Head Loss, Flow & C-Factor Table
Solve the Hazen–Williams equation for head loss, flow, or diameter in US or SI units — with the velocity-form cross-check built into every answer and the full C-factor table below. Pre-loaded with a real exam-style problem.
Switching converts every value into the new system (it doesn't just relabel). Your choice is remembered on this device.
For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.
Quick answer: the Hazen–Williams forms
US: hf = 4.73 · L · Q1.852 / (C1.852 · D4.870) — Q in cfs, D and L in ft
SI: hf = 10.67 · L · Q1.852 / (C1.852 · D4.870) — Q in m³/s, D and L in m
Rearranged: Q = [ hf·C1.852·D4.870 / (K·L) ]1/1.852 · D = [ K·L·Q1.852 / (C1.852·hf) ]1/4.870, with K = 4.73 (US) / 10.67 (SI). The exponents are fixed: 1.852 on Q and C, 4.870 on D — transposing them is a classic error.
Worked example 1 (PE pace): given Q, D, L, C → hf, with cross-check
A 12-in. water main (C = 130) carries 2.0 cfs over 1,000 ft. Find the friction head loss — and verify with the velocity form. This is the calculator's default load; it reproduces every number below.
- D = 12 in = 1.00 ft; A = π(1.00)²/4 = 0.7854 ft²
- hf = 4.73 × 1000 × 2.01.852 / (1301.852 × 1.004.870) = 4.73 × 1000 × 3.610 / 8222.9 = 2.08 ft — gradient 2.08 ft per 1,000 ft
- V = Q/A = 2.0/0.7854 = 2.546 ft/s
- Cross-check: R = D/4 = 0.25 ft; S = hf/L = 0.0020766; V = 1.318 × 130 × (0.25)0.63 × (0.0020766)0.54 = 171.34 × 0.41754 × 0.035593 = 2.546 ft/s ✓ — the two forms agree.
Worked example 2 (FE pace): given hf → Q
The same 12-in. main (C = 130, L = 1,000 ft) shows 2.0766 ft of head loss. Find the flow: set solve-for to Q and enter hf = 2.0766 ft.
- Q = [ 2.0766 × 1301.852 × 1.004.870 / (4.73 × 1000) ]1/1.852 = 2.000 cfs — the exact round-trip of Example 1.
Worked example 3: velocity form (SI)
A 300 mm water main (C = 130) runs on a friction slope of 0.005. Find velocity, discharge, and head loss per kilometre.
- R = D/4 = 0.075 m
- V = 0.85 × C × R0.63 × S0.54 = 0.85 × 130 × 0.0750.63 × 0.0050.54 ≈ 1.24 m/s
- A = π(0.30)²/4 = 0.0707 m² → Q ≈ 0.087 m³/s ≈ 87 L/s
- Head loss = S × L = 0.005 × 1000 = 5.0 m per km
Exam tip: Hazen-Williams is empirical and water-only — if the fluid isn't water near ambient temperature, the exam expects Darcy-Weisbach instead.
Free formula resources
Grab the free formula resources — every FE Civil equation in one searchable index, with the pipe-flow formulas (Hazen–Williams, Darcy–Weisbach, Manning's) on page 1.
C-factor table — and why pipe age matters
C drops as pipe ages. Tuberculation and deposits roughen the wall, so a 40-year-old cast-iron main carries far less than its as-built C suggests. Picking the new-pipe C for an old main is a graded distractor — the exam will give you both numbers and watch which you reach for.
| Pipe material & condition | C range |
|---|---|
| PVC / HDPE plastic | 140–150 |
| New cast iron | 130 |
| Cast iron, 10 yr old | 107–113 |
| Cast iron, 20 yr old | 89–100 |
| Cast iron, 40 yr old | 64–83 |
| New ductile iron, cement-lined | 130–140 |
| Steel, new | 140–150 |
| Steel, 20 yr old | 90–100 |
| Concrete | 120–140 |
| Copper / brass | 130–140 |
| Fire hose with couplings | 100–110 |
When Hazen–Williams is valid — and when the exam wants Darcy–Weisbach
Hazen–Williams is an empirical fit for water at ordinary temperatures in turbulent flow, in typical distribution sizes (about 2 in to 6 ft) and velocities. It needs no Reynolds number and no friction-factor chart, which is exactly why exam problems love it: one equation, no iteration.
Reach for Darcy–Weisbach instead when: the fluid isn't water; the problem gives you a friction factor f or expects you to find one (Moody chart); temperatures are far from ambient; or precision head-loss work is required. If an exam problem hands you C, it's a Hazen–Williams problem; if it hands you f or ε, it's Darcy–Weisbach. The pipe flow topic page works both side by side, and the equation-choice guide drills the stem cues.
Common exam traps
- Diameter in inches plugged into a feet formula. A factor-of-12 slip raised to the 4.87 power is catastrophic — off by roughly 124.87 ≈ 190,000×. The calculator's diameter field is labelled in inches (mm in SI) precisely because of this trap.
- Exponent slips. 1.852 on Q and C, 4.870 on D. Transposing them (or "rounding" to 1.85/4.87 — harmless) vs swapping them (fatal) — keep the pairing straight.
- C picked for the wrong pipe age. New-pipe C = 130 vs 40-year-old C ≈ 74 nearly doubles the head loss. Read the pipe's age in the problem statement.
- Mixing SI/US coefficients. 4.73 (Q in cfs, D in ft) vs 10.67 (Q in m³/s, D in m). The constant and the units travel together.
- Solving for D and stopping at the exact value. Pipes come in nominal sizes — always round up to the next nominal size and re-check hf there. Worked example: Q = 3.0 cfs, L = 2,000 ft, C = 120, allowable hf = 20 ft → exact D = 0.871 ft = 10.45 in; next nominal up is 12 in, at which hf = 10.21 ft — comfortably under the 20 ft allowance, the expected exam conclusion. Try it: set solve-for to D above.
Hazen–Williams — FAQ
Hazen–Williams or Darcy–Weisbach on the exam?
If the problem gives you C, it's Hazen–Williams. If it gives you a friction factor f, a roughness ε, or expects a Moody-chart read, it's Darcy–Weisbach. Hazen–Williams is water-only at ordinary temperatures; anything else forces Darcy–Weisbach.
Why is C lower for old pipe?
Corrosion, tuberculation, and deposits roughen the wall over decades. A cast-iron main drops from C ≈ 130 new to C ≈ 64–83 at 40 years — the same pipe, very different head loss. Always match C to the pipe's stated age.
Can I use it for fluids other than water?
No — the empirical constants were fit to water. For oil, chemicals, or slurries the exam expects Darcy–Weisbach (or a method specific to the fluid).
What are the exponents?
1.852 on Q and C, 4.870 on D. They come from the empirical fit; don't "simplify" them, and don't transpose them.
Nominal or actual inside diameter?
Exam problems use the nominal size as the diameter unless they state an actual ID. In practice, nominal ≠ exact ID for some materials — the calculator notes this and uses the entered value directly, so you can audit it.
Keep building exam speed
Closed-conduit hydraulics shows up across both the FE and the PE Civil WRE exams. The PE WRE Flagship ($119) drills every pipe-flow question type — soft launch, join the waitlist from the contact page. For a full rehearsal under timed conditions, the 110-question FE Civil practice exam ($79) is a 5-hour-20-minute run with detailed solutions.
Last reviewed: 2026-10-03. Formulas follow the NCEES FE Reference Handbook conventions; always confirm against the current handbook.