PSI to GPM Calculator

Article — PSI to GPM Calculator

PSI to GPM calculator: pressure to flow conversion

PSI (pressure) and GPM (flow) are not the same physical quantity, but they relate through the flow coefficient. The two governing equations are Q = Cv × √ΔP for valves and Q = K × √P for sprinklers. Both come from Bernoulli and form the basis of NFPA 13 hydraulic design.

This converter handles both modes. Pick "Valve" when you have a Cv from a manufacturer datasheet. Pick "Sprinkler" when you have a K-factor stamped on a fire sprinkler head. Each mode shows GPM plus L/min, m³/h and CFM so you can read across to whatever unit your project uses.

PSI vs GPM: different quantities

Pressure measures force per unit area. Flow measures volume per unit time. You cannot convert one to the other without a third piece of information — typically the geometry of the orifice or valve the water passes through. Pour from a teapot and a fire hose at the same pressure: you'll get vastly different flow rates because the opening size differs.

The flow coefficient packages that geometry into a single number. For valves it's called Cv. For sprinklers it's K. Both have units of GPM per square root of PSI, so plugging in pressure and taking the square root gives flow directly.

Cv flow coefficient explained

Cv is defined as the flow of water (60°F) through a valve at exactly 1 PSI of pressure drop. A valve with Cv = 25 passes 25 GPM at 1 PSI drop. At 4 PSI drop, the same valve passes 25 × √4 = 50 GPM. Doubling pressure doesn't double flow — pressure scales with the square of velocity, so flow scales with the square root of pressure drop.

Cv comes from the valve manufacturer's datasheet, usually for the fully-open position. Approximate values for common 1-inch valves: ball valve ~25, gate valve ~20, globe valve ~5, check valve ~15. Larger valves scale roughly with the diameter squared.

Sprinkler K-factor (NFPA 13)

Fire-sprinkler engineers use K-factor instead of Cv. It's the same math — gpm per square root of psi — but the convention differs: K is measured at the sprinkler orifice, not across a pressure drop. NFPA 13 lists standard K-factors: 5.6 for ordinary pendant/upright, 8.0 for large orifice, 11.2 for extra-large, 14.0 for ESFR (Early Suppression Fast Response).

A K = 5.6 sprinkler at 40 psi flows 5.6 × √40 = 35.4 GPM. That's the design number used to size mains and pumps. Sprinkler heads have their K-factor stamped on the deflector or recorded in the listing data.

PSI to GPM formula

The two PSI to GPM equations:

For sharp-edge orifices (Pitot-tube hydrant tests), the third formula applies. The discharge coefficient c is typically 0.9 for a smooth outlet, 0.8 for a square outlet, 0.7 for a rough outlet. Diameter d is in inches; result Q is in GPM.

Fire sprinkler design example

Consider a 5,000 ft² office (Light Hazard 1 per NFPA 13). Design density is 0.10 GPM/ft² over a remote area of 1,500 ft². Required flow: 0.10 × 1,500 = 150 GPM. With K = 5.6 sprinklers, each delivering ~35 GPM at 40 psi, the remote area covers about 4 heads.

The hydraulic calculation pushes back from the most remote sprinkler through the pipe network, adding friction loss at each pipe. The final demand at the riser sets the minimum pressure the fire pump must deliver. PSI to GPM math runs at every node.

Irrigation PSI and GPM

Lawn irrigation works at lower pressures. Pop-up spray heads need 30 psi at the nozzle and flow 1-4 GPM. Rotor sprinklers want 45-65 psi and flow 2-12 GPM. Drip emitters operate at 15-30 psi and flow as little as 0.5 GPH (yes, gallons per hour).

The 5-gallon bucket test gives you available flow without any formula: time how long the bucket takes to fill from the source. GPM = 300 / seconds. A 30-second fill is 10 GPM.

Measuring flow with a Pitot gauge

Hydrant flow testing uses a Pitot gauge: a small tube held in the discharge stream measuring velocity pressure. The orifice formula Q = 29.84·c·d²·√P converts the Pitot reading directly to GPM. NFPA 291 specifies the test procedure, including flow-orifice diameters and discharge coefficients.

Static pressure (no flow) gives the maximum available pressure. Residual pressure (during flow) is what's left after friction loss. The difference between static and residual at a known flow tells you the system curve, used in sprinkler hydraulic calculations.

Common PSI to GPM pitfalls

The biggest mistake is treating PSI and GPM as if they're related by a simple multiplier. They aren't — flow scales with the square root of pressure, not linearly. Doubling pressure raises flow by 41%, not 100%. Triple the pressure and you only get 1.73× the flow.

The second mistake is forgetting elevation head. Every 10 vertical feet costs 4.33 psi. A pump rated 50 psi pushing water up a three-story building (30 ft) loses 13 psi to elevation before any flow even starts.

The third trap is reading flow coefficients off the wrong open angle. Cv values quoted on valve datasheets typically apply at fully-open position. A partially closed valve has dramatically lower effective Cv. For modulating valves used in HVAC and process control, manufacturers publish Cv curves showing the relationship between handle position and flow coefficient.

Finally, watch out for fluid mismatches. The Cv formula assumes water at 60°F. For viscous fluids (oil, glycol) you need a viscosity correction. For gases, a different equation applies entirely — the gas Cv formula includes specific gravity and absolute temperature terms because gases compress while liquids do not. Plugging gas flow into the water Cv formula gives wrong answers by 20-50%.