PSI to GPM Calculator
Work out water flow in gallons per minute from the pressure at an orifice, nozzle, hydrant outlet or sprinkler head, using its diameter and discharge coefficient or its K-factor.
GPM = 29.84 × Cd × d² × √PSI · GPM = K × √PSI
Where the 29.84 Comes From
Water leaving an orifice turns its pressure into speed. Bernoulli's equation gives that speed as v = √(2P/ρ). Flow is speed × area, and the discharge coefficient Cd scales it down for the jet narrowing just past the opening.
v = √(2 × 144 × P lb/ft² ÷ 1.94 slug/ft³) = 12.18 × √P ft/s
A = π/4 × d² ÷ 144 ft² · 1 ft³/s = 448.83 gpm
Q = Cd × 0.005454 d² × 12.18 √P × 448.83 = 29.8 × Cd × d² × √P
Fire protection standards round the constant to 29.83 or 29.84. The density of water is built in, so the formula doesn't apply to oil, fuel or air.
Why Twice the Pressure Is Only 41% More Flow
Flow goes with the square root of pressure but the square of diameter. To double the flow you need four times the pressure, or an opening only 1.41 times wider. That's why bigger nozzles, not pumps, are the usual fix for low flow.
| Change | Flow multiplied by |
|---|---|
| Pressure × 2 | 1.41 |
| Pressure × 4 | 2.00 |
| Pressure × 9 | 3.00 |
| Diameter × 1.41 | 2.00 |
| Diameter × 2 | 4.00 |
| Pressure ÷ 2 | 0.71 |
Static vs Flowing Pressure: the Garden Hose Trap
A gauge on a closed tap shows static pressure, say 60 psi. Open the tap and the pressure at the nozzle drops, because the pipes, meter and hose eat some of it as friction. Feed the static 60 psi into the formula with a ½ in opening and you get over 40 gpm, several times more than a household supply can deliver.
Use the pressure measured at the outlet while it flows. For example, if a 3/16 in nozzle (Cd 0.95) reads 40 psi while spraying:
For flow through a length of pipe, which depends on its length and roughness, use a pipe-friction method such as Hazen-Williams instead.
Worked Example: a Hydrant Flow Test
A crew opens a 2½ in hydrant outlet and holds a pitot gauge in the stream, which reads 36 psi. The outlet is smooth and well rounded, so NFPA 291 gives c = 0.90. (This is the orifice mode's Load Example.)
Step 1: Diameter squared
Step 2: Square root of the pitot pressure
Step 3: Multiply
The outlet is flowing about 1,000 gpm (3,810 L/min). The test also records how far the residual pressure at a nearby hydrant drops, which is used to estimate the flow available at 20 psi residual.
NFPA 291 uses c = 0.90 for smooth, well-rounded outlets, 0.80 for square, sharp outlets, and 0.70 for outlets that project into the barrel. Those are the first three presets above.
Sprinkler K-Factors
Sprinkler heads, spray nozzles and emitters are rated by a K-factor instead of a diameter, which folds the opening size and Cd into one number: GPM = K × √psi. NFPA 13 sets 7 psi as the minimum operating pressure for a standard sprinkler. Metric datasheets use L/min per √bar, about 14.4 times the US figure.
| K (US) | Metric | At 7 psi | At 15 psi | At 50 psi | Typical use |
|---|---|---|---|---|---|
| 5.6 | K80 | 14.8 gpm | 21.7 gpm | 39.6 gpm | Standard ½ in head, light hazard |
| 8 | K115 | 21.2 gpm | 31 gpm | 56.6 gpm | Ordinary hazard, larger orifice |
| 11.2 | K160 | 29.6 gpm | 43.4 gpm | 79.2 gpm | Extra hazard and storage |
| 14 | K200 | 37 gpm | 54.2 gpm | 99 gpm | Storage (CMSA heads) |
| 25.2 | K360 | 66.7 gpm | 97.6 gpm | 178.2 gpm | ESFR warehouse heads |
Real sprinkler design also sets a minimum density and covers the pipe losses back to the supply. This table only shows what one head discharges at a given pressure.
Pressure Washer Nozzle Numbers
Pressure washer tips are sold by a size number such as 040, which means 4.0 gpm at 4,000 psi. That makes the K-factor 4.0 ÷ √4,000 = 0.0632. On a 3,000 psi machine the same tip passes 0.0632 × √3,000 = 3.46 gpm.
Matching works the other way too. Divide the machine's rated gpm by √(rated psi), multiply by √4,000 and by 10, and pick the nearest size. A tip that's too small pushes pressure above the pump's rating; one that's too big drops the pressure.
Frequently asked questions
Can I convert PSI to GPM without knowing the opening size?
No. Pressure alone doesn't set flow; the same 50 psi pushes a trickle through a pinhole and hundreds of gpm through a hydrant outlet. You need the diameter and Cd, or a K-factor.
What discharge coefficient should I use for a drilled hole?
About 0.61 for a clean, sharp-edged hole in a thin plate. Burrs or a thick wall change it, so measure the flow with a bucket and timer if accuracy matters.
Does this work for bar and litres per minute?
Yes. Pick bar and mm in the unit menus; the calculator converts internally and shows L/min and m³/h, plus the metric K-factor.
Why is my measured flow lower than the calculator says?
Usually because the pressure you entered was the static pressure, or was measured away from the outlet. Measure as close to the opening as you can, with water flowing.
Sources
- NFPA 291, Recommended Practice for Water Flow Testing and Marking of Hydrants: Q = 29.83 c d² √p and outlet coefficients of 0.90, 0.80 and 0.70.
- NFPA 13, Standard for the Installation of Sprinkler Systems: Q = K √P, nominal K-factors and the 7 psi minimum operating pressure.
- Crane Technical Paper No. 410, Flow of Fluids Through Valves, Fittings and Pipe: orifice discharge coefficients and the derivation from Bernoulli's equation.
Related Tools
Convert BTU per hour to tons of refrigeration.
Convert joules, calories, kilowatt-hours, and more.
Convert liters per minute to other flow rate units.
Convert newtons, pounds-force, dynes, and more.
Convert between hertz, kilohertz, megahertz, and more.
Convert torque from in-lb to ft-lb.