PSI to GPM Calculator
Convert a pressure reading to a flow rate. Enter the pitot or gauge pressure in psi, the orifice or nozzle diameter in inches, and the outlet type to get GPM, liters per minute, gallons per hour, and jet velocity.
Example: with Pressure (psi) 50 · Orifice / nozzle diameter (in) 0.625 · Outlet type (discharge coefficient) Smooth, rounded outlet (c = 0.90) → Flow rate: 74.2 GPM.
- Metric flow281 L/min
- Per hour4,449 gallons per hour
- Jet velocity86.2 ft/s jet velocity
Computed by the calculator below using its default values. Change any input to see your own numbers.
Q = 29.83 × c × d² × √p — the hydrant discharge formula from NFPA 291. It converts pressure to flow only through a known opening; psi alone never determines GPM in a pipe system.
What PSI-to-GPM actually means
Pressure and flow are not two units of the same thing — you cannot convert one to the other without knowing the opening the water passes through. What you can do is what fire crews do at hydrants: read the velocity pressure with a pitot gauge at a known outlet and compute flow with Q = 29.83 × c × d² × √p (NFPA 291). The d² term is the geometry (double the diameter, four times the flow) and √p is the physics — flow grows with the square root of pressure, so doubling pressure only buys about 41% more water.
The coefficient c corrects for how cleanly the jet leaves the opening: 0.90 for smooth rounded outlets, 0.80 for square edges, 0.70 for sharp or projecting ones.
Using it beyond hydrants
The same orifice math works for nozzles, drilled manifolds, and open pipe ends where you know pressure at the opening. What it will not do is tell you a house's or pump's delivery: in a real system, friction in pipe and fittings eats pressure as flow rises, so available GPM depends on the whole path, not the gauge reading at rest. Static pressure with no flow says almost nothing — it is the residual pressure while flowing that matters. Pair this with a friction-loss calculation for system questions.
How it’s calculated
Q (GPM) = 29.83 × c × d² × √p, with d = orifice diameter in inches and p = pitot (velocity) pressure in psi — NFPA 291 hydrant flow formula; c = 0.90 / 0.80 / 0.70 by outlet type. L/min = GPM × 3.78541; GPH = GPM × 60. Jet velocity = 12.19 × √p ft/s (from v = √(2gh) with h = 2.31 ft of head per psi).
Assumes the pressure is measured at the discharge (pitot) of a full-flowing circular opening — upstream gauge readings on a piped system include friction and give optimistic flows.
Flow through a 3/4 in smooth outlet (c = 0.90)
| Pressure | Flow |
|---|---|
| 20 psi | 67.5 GPM |
| 40 psi | 95.5 GPM |
| 60 psi | 117.0 GPM |
| 80 psi | 135.1 GPM |
| 100 psi | 151.0 GPM |
Computed with Q = 29.83 × 0.9 × 0.75² × √p; note flow grows with the square root of pressure.
Common mistakes
- Treating psi as convertible to GPM without a diameter — a 60 psi reading flows 4x more water through a 1 in opening than a 1/2 in one.
- Using static pressure from a gauge on a closed system; the formula wants the velocity (pitot) pressure of moving water at the outlet.
- Forgetting the square root: doubling pressure does not double flow, it adds about 41%.
- Applying orifice flow to a long hose or pipe run — friction loss dominates there, and actual delivery is far below the orifice number.
Frequently asked questions
What is the PSI to GPM formula?
Q = 29.83 × c × d² × √p, where d is the orifice diameter in inches, p is pitot pressure in psi, and c is a discharge coefficient (0.90 smooth, 0.80 square, 0.70 sharp). It is the hydrant flow-test formula from NFPA 291.
Can I convert PSI to GPM directly?
No — they measure different things (pressure versus volume per time). Flow only follows from pressure once you fix the opening size and shape, which is exactly what the diameter and coefficient inputs do.
Why does flow rise with the square root of pressure?
Water speed through an opening follows v = √(2gh) — kinetic energy trades against pressure head. Since flow is speed × area, quadrupling pressure is needed to double the flow through the same hole.
What coefficient should I pick?
0.90 for smooth, rounded outlets like hydrant butts in good condition and tapered nozzles; 0.80 for square, cleanly cut openings; 0.70 for sharp-edged or inward-projecting outlets. When unsure, 0.80 is the conservative middle.
Why is my well or house GPM lower than this?
Because a plumbing system is not a single orifice: every foot of pipe, elbow, and valve burns pressure as flow increases. Measure real delivery with a bucket test, and use a friction-loss calculator to see where the pressure goes.