Convert pressure to flow rate using the orifice equation or the valve Cv method with live results in GPM, L/min, m³/h and more.
Q = Cd × A × √(2 × ΔP / ρ) — where Q is flow, Cd is the discharge coefficient, A is the orifice area, ΔP is the pressure drop in pascals, and ρ is the fluid density (SG × 1000 kg/m³).| Unit | Symbol | Value |
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| Property | Value |
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| # | Flow (GPM) | Input | Time |
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PSI to GPM conversion is the process of calculating liquid flow rate through a restriction from the pressure drop across it. The pressure drop in pounds per square inch drives the fluid through an orifice, valve, or fitting, and the resulting flow depends on the opening size, the fluid’s density, and the discharge characteristics of the restriction. The relationship is the basis of hydraulic system design, fire sprinkler sizing, and flow meter calibration.
Engineers use two math paths. The orifice equation models flow through a fixed hole with a known discharge coefficient. The valve Cv method uses the manufacturer’s published flow coefficient for a specific valve at a specific opening. Both are approximations of the same physics: pressure energy converts to kinetic energy as the fluid accelerates through the restriction, and the flow rate follows from the geometry and the fluid properties. The International Organization for Standardization codifies the orifice method in ISO 5167, and the International Society of Automation publishes the valve sizing standard ISA-75.01.01.
You convert PSI to GPM by applying either the orifice equation or the valve Cv equation, depending on whether the flow restriction is a fixed hole or a control valve. The orifice method needs the hole diameter and discharge coefficient. The valve method needs the manufacturer’s Cv rating. Both methods need the pressure drop and the fluid’s specific gravity.
Pick the method: Orifice flow for a fixed restriction with a measured or specified hole size, or Valve Cv for a control valve, ball valve, or fitting with a published flow coefficient.
Enter the pressure drop in PSI. This is the differential across the restriction, not the upstream gauge pressure.
Enter the fluid’s specific gravity. The presets cover water (1.00), gasoline (0.74), diesel (0.85), and oil (0.90). For other fluids, type the value directly.
For orifice flow, enter the orifice diameter in inches. A typical garden hose orifice is 0.25–0.5 in; a fire sprinkler head is 0.375–0.625 in.
For orifice flow, confirm the discharge coefficient. Sharp-edged orifices run 0.61. Rounded entrances run 0.80. Smooth nozzles run 0.95–0.98. The preset buttons cover the common cases.
For valve flow, enter the Cv rating from the manufacturer’s datasheet. Cv is the flow of water in GPM at 60°F with a 1 PSI pressure drop across the fully open valve.
Read the result in the hero panel, then check the quick grid for L/min, m³/h, and L/s. The full unit table shows eleven flow units.
The formula depends on the method. Orifice flow uses the discharge coefficient, the hole area, and the fluid density. Valve flow uses the manufacturer’s Cv rating and the fluid’s specific gravity.
Formula (orifice): Q = Cd × A × √(2 × ΔP ÷ ρ)
Formula (valve): Q = Cv × √(ΔP ÷ SG)
In the orifice form, Cd is the discharge coefficient, A is the orifice area in square metres, ΔP is the pressure drop in pascals, and ρ is the fluid density in kg/m³. The result is flow in cubic metres per second, which the calculator converts to GPM. In the valve form, Cv is the valve coefficient, ΔP is in PSI, SG is the specific gravity relative to water at 60°F, and the result is directly in GPM. The two formulas are not interchangeable, they answer different questions about different restrictions.
Suppose you’re checking the flow through a fire sprinkler head rated for 150 PSI operation. The orifice diameter is 0.5 in, the discharge coefficient for a standard sprinkler head is approximately 0.95, and the fluid is water at SG = 1.00. You want the flow rate in GPM and L/min.
Step 1. Select Orifice flow as the method.
Step 2. Enter 150 for the pressure drop in PSI.
Step 3. Leave SG at 1.00, the tool defaults to water.
Step 4. Enter 0.5 for the orifice diameter.
Step 5. Set Cd to 0.95 using the smooth nozzle preset.
Step 6. The calculator converts 150 PSI to 1,034,213.59 Pa.
Step 7. It computes the orifice area: π/4 × (0.5 × 0.0254)² = 1.267 × 10⁻⁴ m².
Step 8. It applies the orifice equation: 0.95 × 1.267 × 10⁻⁴ × √(2 × 1,034,213.59 ÷ 1,000) = 0.02649 m³/s.
Step 9. It converts to GPM: 0.02649 × 15,850.32 = 419.9 GPM.
Step 10. The quick grid shows the same flow as 419.9 GPM, 1,589.5 L/min, 95.4 m³/h, and 26.5 L/s.
The result tells you the sprinkler head flows about 420 GPM at 150 PSI. Fire protection standards typically rate sprinkler heads by their K-factor, which is the flow in GPM divided by the square root of the pressure in PSI. The K-factor here is 420 ÷ √150 = 34.3, which is consistent with a large-orifice sprinkler head. For a standard 1/2-inch head with a K-factor of 5.6, the flow at 150 PSI would be much lower. The conversion confirms which head you’re working with.
This table lists typical flow rates for common liquid systems where PSI-to-GPM calculations drive sizing decisions. The values are drawn from published industry references and manufacturer data; they are context for interpreting a converted result, not outputs of the calculator.
| Application | Typical Flow Rate |
|---|---|
| Kitchen faucet aerator | 1.5–2.2 GPM |
| Shower head (low-flow) | 1.5–2.5 GPM |
| Garden hose (standard) | 5–10 GPM |
| Residential water service line | 10–20 GPM |
| Residential fire sprinkler head | 15–40 GPM |
| Commercial fire sprinkler head | 40–150 GPM |
| Fire hydrant | 500–1,500 GPM |
| Pivot irrigation sprinkler | 5–20 GPM per head |
| Hydraulic pump (small mobile) | 5–20 GPM |
| Hydraulic pump (industrial) | 20–100 GPM |
| Automotive fuel injector | 0.02–0.05 GPM per injector |
| Diesel engine fuel return line | 0.5–2 GPM |
| Residential pool pump | 30–80 GPM |
The formula is exact for ideal conditions, but real hydraulic systems deviate in predictable ways. These are the practical factors that separate a calculated flow rate from the flow rate you’ll measure on a flow meter.
Discharge coefficient uncertainty. For a sharp-edged orifice, Cd is 0.61 ± 0.01. That 1.6% uncertainty propagates directly into the flow rate. For a nozzle or venturi, Cd is higher and more consistent, but still not perfect.
Pressure drop measurement. The ΔP across a restriction is often inferred from upstream and downstream gauges. Gauge accuracy of ±1% on each reading produces a ±2% pressure error, which propagates as ±1% in flow (since Q scales with the square root of ΔP).
Fluid viscosity. The orifice and Cv equations assume fully turbulent flow. At low Reynolds numbers thin fluids, small orifices, low flow rates, viscosity matters and the equations over-predict flow. Standard references such as ISO 5167 define the Reynolds number ranges where the standard Cd values apply.
Cavitation and flashing. When the downstream pressure drops below the fluid’s vapour pressure, vapour bubbles form, and the actual flow is lower than the formula predicts. Cavitation is common in high-pressure-drop valve applications and can damage the valve.
Specific gravity at operating temperature. SG values in reference tables are usually at 60°F. At 150°F, hydraulic oil is thinner and its SG is slightly different. For tight work, use the SG at the operating temperature.
Viscous fluids. The Cv method assumes water-like viscosity. For fluids above about 10 centistokes, the International Society of Automation sizing standard requires a viscosity correction factor. Motor oil, heavy fuel oil, and glycerin all fall into this category.
Valve opening position. A valve’s Cv changes with its position. A fully open ball valve and a half-open ball valve have very different Cv values. The catalogued Cv is the fully open value.
You can’t convert PSI to GPM directly, they measure different things. You need either an orifice specification (diameter and Cd) or a valve Cv rating, plus the fluid’s specific gravity. With those inputs, the orifice equation or the Cv equation gives the flow rate.
The orifice formula is Q = Cd × A × √(2 × ΔP ÷ ρ), where Q is in m³/s, Cd is dimensionless, A is in m², ΔP is in Pa, and ρ is in kg/m³. The valve formula is Q = Cv × √(ΔP ÷ SG), where Q is in GPM, Cv is the valve coefficient, ΔP is in PSI, and SG is dimensionless.
That depends on the restriction. A 1/2-inch sharp-edged orifice at 100 PSI flows about 13 GPM of water. The same orifice at 50 PSI flows about 9 GPM. A valve with Cv = 10 flows exactly 100 GPM at 100 PSI with water.
Cv is the valve flow coefficient. It’s defined as the flow of water in GPM at 60°F through a fully open valve with a 1 PSI pressure drop. A higher Cv means a larger valve or a more open one.
Cd is a dimensionless number that accounts for friction and turbulence losses in a real orifice. A perfect frictionless orifice would have Cd = 1.0. A sharp-edged orifice has Cd ≈ 0.61 because the flow contracts as it exits. A smooth nozzle has Cd ≈ 0.98 because it guides the flow with minimal losses.
Yes. Flow scales with the inverse square root of SG. A fluid with SG = 0.74 (gasoline) flows about 16% faster than water through the same restriction at the same pressure drop. A fluid with SG = 1.20 flows about 9% slower.
No. The orifice and Cv equations on this page are for incompressible liquids. Gas flow requires additional terms for the gas’s compressibility factor, the expansion factor, and the ratio of specific heats. Use a dedicated gas flow calculator for air, steam, or natural gas.
The K-factor is the flow in GPM divided by the square root of the pressure in PSI. A sprinkler head with K = 5.6 flows 5.6 GPM at 1 PSI, 22.4 GPM at 16 PSI, and 56 GPM at 100 PSI. The K-factor combines the orifice diameter and the discharge coefficient into one number.
Look on the manufacturer’s datasheet. Every industrial valve ships with a published Cv rating, and most manufacturers post the value on their website. For ball valves, Cv depends on the bore size; for control valves, Cv is given at various opening percentages.
The most common causes are incorrect Cd, incorrect Cv, partial valve opening, pipe friction losses not accounted for, cavitation, or fluid viscosity higher than the equation assumes. Check each input against the actual system, then verify with a flow meter.
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