Formula
Flow is volume per time. A bucket is gallons divided by seconds, times 60. Pipe flow is velocity times the inside area. The area is π times the diameter in feet, squared, divided by 4. Multiplying by 448.831 turns cubic feet per second into gallons per minute. The short form is about 2.448 × velocity × diameter squared, with the diameter in inches.
GPM = gallons ÷ seconds × 60
GPM = velocity × area × 448.831
GPM = 29.83 × c × diameter² × √psi
minutes = gallons ÷ GPM
An open outlet is not a pipe network. The 29.83 factor is the hydrant-flow form in NFPA 291: coefficient, diameter in inches, and the square root of the residual pressure. A smooth outlet or a hydrant butt is about 0.90. A square edge is about 0.80. A projecting outlet is about 0.70. Friction along a pipe is a different calculation.
Cold-water velocity is often kept around 5 to 8 feet per second so the pipe stays quiet. Hot water in copper is often kept slower, because velocity and temperature wear the tube. That is handbook guidance, not a code limit. A showerhead’s federal maximum is 2.5 GPM at 80 psi, and a lavatory faucet’s is 2.2 GPM at 60 psi. Those are fixture limits, not the flow of your house.
Worked examples
5 gallons in 30 seconds. 10.0 GPM, 37.85 L/min, 600 gal/hr. 2.5 gallons in 20 seconds. 7.5 GPM.
1.000 in ID at 5 ft/s. 12.24 GPM. 10 GPM in a 0.75 in ID. 7.26 ft/s.
2.5 in outlet, coefficient 0.90, 50 psi. About 1,186 GPM, as free discharge.
20,000 gallons at 10 GPM. 2,000 minutes, 33 hours and 20 minutes.
10 GPM. 37.854 L/min, 2.271 m³/h, 0.02228 ft³/s.
Reference
At 5 ft/s, Schedule 40 inside diameters from the pipe table give about 4.74 GPM at ½ inch nominal and 8.31 GPM at ¾ inch. Copper type L at ½ inch is about 3.64 GPM at the same speed, because the bore is smaller.
Questions
How do I calculate GPM?
Divide the gallons by the seconds and multiply by 60. Five gallons in 30 seconds is 10.0 GPM. Run the bucket three times and average the times if the stream is uneven.
How many GPM does a ½ inch or ¾ inch pipe carry?
It depends on the velocity and the real inside diameter, not the nominal size. At 5 ft/s, Schedule 40 at about 0.622 in ID is 4.74 GPM, and at about 0.824 in ID it is 8.31 GPM. Copper type L at ½ inch is a smaller bore, about 3.64 GPM at the same speed. Pressure and friction still decide what you actually get.
What is a good water flow rate for a house?
A fixture has a published maximum, not a target this page assigns. Federal showerheads are limited to 2.5 GPM at 80 psi, and lavatory faucets to 2.2 GPM at 60 psi. A whole house depends on the pressure, the pipe, and how many fixtures run at once.
How do I convert GPM to litres per minute?
Multiply by 3.785411784. Ten GPM is 37.854 L/min, about 2.271 cubic metres per hour, and about 0.02228 cubic feet per second.
How long does a garden hose take to fill a pool?
Divide the gallons by the GPM. Twenty thousand gallons at 10 GPM is 2,000 minutes, 33 hours and 20 minutes. The pool volume calculator can give you the gallons. A hose is often slower than 10 GPM. Time it with the bucket.
How do I calculate flow from pressure and pipe diameter?
An open outlet uses 29.83 times a discharge coefficient times the diameter squared times the square root of the pressure. That is free discharge, not the flow through a long pipe. A pipe run loses pressure to friction. That loss is the friction-loss calculator.
What is the difference between flow rate and water pressure?
Pressure is the push, in psi. Flow is the volume per time, in GPM. A closed faucet can have pressure and no flow. Opening it trades some of that pressure for flow, and the pipe size decides how much.
Sources
- Copper Development Association, Copper Tube Handbook. The velocity note, about 5–8 ft/s for cold water and a lower speed for hot water, is that handbook’s design guidance. It is not a code limit. Tube walls for types L and M are the ASTM B88 nominals already used on the pipe-volume page.
- Schedule 40 inside diameters are the ASME B36.10 figures on the pipe-volume page. PVC Schedule 40 in the common small sizes uses those same outside diameters and walls. The stamp on the pipe wins. PEX is ASTM F876 SDR-9, wall equal to the outside diameter divided by 9.
- NFPA 291, the recommended practice for fire flow testing and marking of hydrants. The open-outlet formula Q = 29.83 × c × d² × √p is that discharge equation. This page uses it only for free discharge. It is not a fire-flow test and not a sprinkler design.
- 10 CFR 430.32 and EPA WaterSense. The federal showerhead maximum cited here is 2.5 GPM at 80 psi, and the lavatory faucet maximum is 2.2 GPM at 60 psi. NIST SP 811 supplies 3.785411784 litres per gallon. One cubic foot per second is 448.831 GPM from 7.48052 gallons per cubic foot.