Flow rate and velocity: the starting point
Every pipe flow question starts from continuity — the flow rate is the average velocity multiplied by the cross-sectional area of the bore:
So 40 gpm through a pipe with a 2 in inside diameter runs at 0.4085 × 40 ÷ 2² = 4.09 ft/s. Turn that around and a 6 in bore at 5 ft/s carries about 0.982 cfs, which is roughly 441 gpm. The water flow rate and the pipe velocity are two views of the same number once you know the diameter, which is why getting the inside diameter right matters before anything else.
Use the actual inside diameter, not the nominal size
This is the single most common error in any pipe flow calculator. The nominal size stamped on a pipe is a trade label, not the bore: the true inside diameter depends on the material, the wall thickness and the schedule. Because diameter is raised to about the 4.87 power in the friction formulas, even a small diameter slip becomes a large error in flow rate or head loss. For that reason this tool deliberately ships no nominal-size lookup — you enter or measure the real inside diameter, and every result is computed from that.
Hazen-Williams: friction loss for water
For water at ordinary temperatures, the Hazen-Williams equation gives friction head loss directly. In US units the loss per 100 ft is:
The coefficient C captures roughness: smooth new plastic is around 150, copper near 140, newer steel about 120, and old cast iron drops toward 100. A worked check: 200 gpm in a 3.068 in bore at C = 140 gives a loss of about 9.0 ft per 100 ft. Note that the Hazen-Williams constant changes with the unit system — you'll see roughly 4.73 in cubic-feet-per-second form, 0.2083 in the per-100-ft form above, 4.52 in the fire-protection form, and 10.67 in SI — so a result is only meaningful when the constant matches the units, which the tool handles for you.
Where Hazen-Williams stops being honest
Hazen-Williams is empirical and was fitted to water flowing at roughly 2–10 ft/s at about 40–75 °F. Outside that — air, gas, hot water, oil or slurry, or very slow or very fast flow — it quietly drifts off. That's the honest limitation: it's a water formula, not a universal one, so the calculator flags when your velocity leaves the valid band and suggests switching to Darcy-Weisbach.
Darcy-Weisbach: any fluid, with viscosity
Darcy-Weisbach is the general friction equation. It works for any fluid because it uses the absolute roughness ε and the fluid's viscosity rather than a water-only coefficient:
The Reynolds number tells you which regime you're in: below about 2300 the flow is laminar, above about 4000 it's turbulent, and the 2300–4000 band is an unstable transition. The default kinematic viscosity is for water near 60 °F (about 1.21×10⁻⁵ ft²/s, or 1.12×10⁻⁶ m²/s), and it's editable for warmer water or other fluids. Typical absolute roughness values, in mm: drawn plastic about 0.0015, commercial steel about 0.045, galvanized about 0.15, cast iron about 0.26, concrete roughly 0.3–3.
Manning: gravity and partially-full pipe
When a pipe isn't pressurised — a drain, sewer or culvert running part-full by gravity — Manning's equation is the right tool:
A frequent 100× error here is entering the slope wrong: a 1 % slope is 0.01 as a decimal, so typing 1 where the formula wants 0.01 overstates velocity badly. This tool lets you enter slope as a percent or a decimal and converts, so that trap is closed. For a partially-full circular pipe it computes the flow area and wetted perimeter from your depth-to-diameter ratio using the circular-segment geometry.
What's a sensible velocity?
Friction loss isn't the only limit — velocity itself has comfort and durability bounds. The figures below are general rules of thumb, not a code requirement; the calculator flags where your number sits.
| Service | Guideline velocity |
|---|---|
| Cold water service | 4–8 ft/s |
| Hot water (below ~140 °F) | 3–5 ft/s |
| Hot water (above ~140 °F) | 2–3 ft/s |
| General commercial | up to ~10 ft/s |
| Fire flow (short duration) | 10–15 ft/s |
Too slow (below about 2 ft/s) can leave air trapped; too fast brings noise, water hammer and erosion. Above roughly 140 °F, hot water becomes aggressive and velocities are kept lower to limit erosion-corrosion.
Straight-pipe friction is not the whole story
The friction figure from any of these methods is for the straight pipe only. Real systems also lose head at valves, bends, entrances, exits and other fittings — the minor losses — and gain or lose head with elevation change, which is separate again. The optional add on the calculator lets you total a set of K-factors (loss = ΣK · V²÷2g) or an equivalent pipe length, and reports that loss on its own so you can always see what's pipe and what's fittings.
Turning head loss into pressure drop
For water, head in feet converts to pressure simply: ΔP (psi) = h_f (ft) × 0.4332. In SI, ΔP (kPa) = ρ × g × h_f ÷ 1000. So 9 ft of head loss is about 3.9 psi. The calculator shows both the head loss and the equivalent pressure drop.
Worked examples
Example 1 — velocity from flow
40 gpm in a 2 in inside diameter: V = 0.4085 × 40 ÷ 2² = 4.09 ft/s, comfortably inside the cold-water band. Load it with ?method=dw&q=40&qunit=gpm&id=2&idunit=in.
Example 2 — Hazen-Williams head loss
200 gpm through 100 ft of 3.068 in bore at C = 140 loses about 9.0 ft (≈3.9 psi). Try ?method=hw&solve=headloss&q=200&qunit=gpm&id=3.068&idunit=in&C=140&len=100&lenunit=ft.
Pipe flow FAQ
How do I calculate water flow rate from pipe size and velocity?
Flow rate is velocity times cross-sectional area: Q = V × A, where A = π × ID² ÷ 4. A handy US shortcut is V (ft/s) = 0.4085 × Q (gpm) ÷ ID (in)², so a 2 in inside-diameter pipe carrying 40 gpm runs at about 4.09 ft/s. The flow-rate tab does this and reports gpm, cfs, L/s and m³/s at once. Always use the true inside diameter, not the nominal pipe label.
Why do I need the actual inside diameter and not the nominal pipe size?
Nominal pipe size is a trade label, not the bore. The real inside diameter depends on material, wall thickness and schedule, and can differ from the nominal number by a noticeable amount. Because diameter is raised to roughly the 4.87 power in the friction equations, a small diameter error turns into a large flow or head-loss error — the single most common mistake people make. This tool never guesses an inside diameter from a nominal size; you enter the real bore and it works from that.
What is the Hazen-Williams formula for friction loss in a pipe?
In US units the head loss per 100 ft is h₁₀₀ = 0.2083 × (100 ÷ C)^1.852 × Q^1.852 ÷ d^4.8655, with Q in gpm and d in inches; total loss is h₁₀₀ × L ÷ 100. In SI it's h_f = 10.67 × L × Q^1.852 ÷ (C^1.852 × d^4.87), with Q in m³/s, d and L in metres. C is the roughness coefficient: higher for smooth new plastic, lower for old rough metal. The tool shows the worked figure so you can check it by hand.
When should I use Darcy-Weisbach or Manning instead of Hazen-Williams?
Hazen-Williams is empirical and valid only for water at ordinary temperatures (about 40–75 °F) flowing at roughly 2–10 ft/s. For air, gas, hot water, oil, glycol or slurry, or velocities outside that band, use Darcy-Weisbach, which takes roughness and viscosity and works for any fluid. For gravity flow that doesn't fill the pipe, like a drain or culvert, use Manning. The calculator warns when Hazen-Williams is pushed outside its valid range and points to the other methods.
What is a good water velocity in a pipe?
Common rules of thumb are roughly 4–8 ft/s for cold water service, about 3–5 ft/s for hot water (lower above about 140 °F to limit erosion), up to about 10 ft/s for general commercial flow, and 10–15 ft/s for short-duration fire flow. Too slow can leave air trapped; too fast brings noise, water hammer and erosion. These are general guidelines, not a code requirement, and the tool flags where your velocity falls.
Does this calculator include fitting and valve losses?
Only if you ask it to, and clearly labelled as separate. The main result is straight-pipe friction loss. Real systems also lose head at valves, bends, entrances, exits and other fittings (minor losses), and gain or lose head with elevation — these aren't part of the straight-pipe figure. The optional minor-loss add lets you enter a sum of K-factors or an equivalent length and reports that loss on its own, so you can see what's pipe and what's fittings.
Is this pipe flow calculator free and private?
Yes. It's free, needs no signup or download, and runs entirely in your browser, so nothing you enter leaves your device. You can copy a shareable link that reopens the calculator with your method, inside diameter, flow and length already filled in.