Pipe Water Flow Rate Calculator: GPM from pipe size and pressure (Hazen-Williams)
Find how much water a pipe can carry from its inside diameter, length, material and the pressure you can lose to friction (Hazen-Williams), the pressure loss at a given flow, or the flow from pipe size and velocity. Results in GPM, L/min and m³/h with velocity, head loss and a pipe-size table.
How it works
Hazen-Williams (NFPA 13 / plumbing form): p = 4.52 × Q^1.85 ÷ (C^1.85 × d^4.87), p in psi per foot, Q in gpm, d = inside diameter in inches (metric form: p = 6.05 × 10^5 × Q^1.85 ÷ (C^1.85 × d^4.87) in bar/m, Q in L/min, d in mm) · Flow from pressure: Q = (p × C^1.85 × d^4.87 ÷ 4.52)^(1 ÷ 1.85), with p = (available psi − 0.433 × rise in ft) ÷ (length × (1 + fittings %)) · Velocity V (ft/s) = 0.4085 × Q ÷ d² · Flow from velocity Q = 2.448 × d² × V · 1 psi = 2.307 ft of water
How much water a pipe delivers depends on how much pressure you can afford to lose to friction along it. The Hazen-Williams equation links flow, inside diameter, pipe roughness (the C factor) and friction loss for water at normal temperatures; this calculator uses the form printed in NFPA 13 and plumbing design texts, p = 4.52 Q^1.85 ÷ (C^1.85 d^4.87). Choose “Flow rate from pressure drop” to find the flow a run can carry, “Pressure loss at a flow rate” to check a design flow, or “Flow rate from velocity” for the simple continuity relation Q = area × velocity. Because the diameter enters to the 4.87 power, size matters far more than anything else: one pipe size up carries roughly 60–110% more water at the same pressure loss, and doubling the bore carries about 6 times as much. Always use the real inside diameter, which differs from the nominal size and between copper types, PEX and PVC schedules. The C factor falls as pipes age and scale up, which is why old galvanized lines lose so much flow. The result counts only straight-pipe friction. Elbows, tees and valves add equivalent length (enter an allowance under More options), lifting water uses 0.433 psi per foot of rise, and the pressure you spend must leave enough at the fixture (often 8–20 psi). Hazen-Williams is empirical and meant for water near room temperature; for hot water, other liquids or very small or slow flows, use Darcy-Weisbach.
Worked example
A 1 in inside-diameter copper line (C = 140), 100 ft long, with 5 psi to spend on friction (the defaults): the friction rate is 5 ÷ 100 = 0.05 psi/ft. Solving Hazen-Williams for flow, Q = (0.05 × 140^1.85 × 1^4.87 ÷ 4.52)^(1/1.85) = (0.05 × 9,337 ÷ 4.52)^0.5405 = 103.3^0.5405 ≈ 12.3 GPM (about 736 gal/hour, 46 L/min). The velocity is 0.4085 × 12.27 ÷ 1² ≈ 5.01 ft/s, fine for cold water but slightly above the usual 5 ft/s limit for hot water. The same 5 psi through a 3/4 in bore gives only about 5.8 GPM.
Sources: Open Exam Prep (NICET): The Hazen-Williams friction loss equation, NFPA 13 form with worked examples · Engineering ToolBox: Hazen-Williams equation, friction loss in water pipes · Engineering ToolBox: Hazen-Williams coefficients (C values by material) · Hazen-Williams equation (Wikipedia) · BCcampus Plumbing: water pipe sizing and the Hazen-Williams formula
Frequently asked questions
How many GPM can a 1 inch pipe carry?
It depends on length and pressure. With 5 psi of friction loss per 100 ft, a 1 in bore of copper or PEX carries about 12 GPM at 5 ft/s; at the common 8 ft/s velocity limit it carries about 20 GPM. A 3/4 in bore carries about half as much at the same pressure loss.
What water velocity is safe in a pipe?
Aim for under about 8 ft/s (2.4 m/s) on cold lines and 5 ft/s (1.5 m/s) on hot lines. Faster water is noisy, causes water hammer and erodes copper and fittings over the years. The calculator warns you above these limits.
What is the C factor?
C is the Hazen-Williams roughness coefficient: higher means smoother. PVC and CPVC are about 150, copper, PEX and polyethylene about 140, new cast iron about 130, galvanized iron about 120, and 20–30-year-old cast iron drops to about 75–100 as scale builds up.
Does this include fitting losses?
Only if you add them. Each elbow, tee and valve adds resistance equal to several feet of extra pipe, so enter a fittings allowance (often 25–50% of the straight length) under More options. Water meters and backflow preventers take extra pressure on top.
How do I find the pressure loss for a known flow?
Choose “Pressure loss at a flow rate”. For example, 500 GPM through 125 ft of 4.026 in steel pipe with C = 120 loses 4.52 × 500^1.85 ÷ (120^1.85 × 4.026^4.87) = 0.0718 psi/ft, or about 8.97 psi in total.
Why is my answer different from Darcy-Weisbach?
Hazen-Williams is an empirical fit for water near room temperature and turbulent flow. Darcy-Weisbach uses the fluid’s viscosity and the pipe’s absolute roughness and works for any fluid. For normal plumbing and irrigation sizes the two usually agree within about 10%.
Related calculators
Estimates for planning only. Size water supply piping to your local plumbing code (fixture units, minimum outlet pressure) or have a licensed plumber or engineer check the design.