PSI to GPM Calculator

Psi to gpm is one of the most commonly misunderstood phrases in plumbing and pump conversations. It sounds like a unit conversion, but it is not. Pounds per square inch describe pressure. Gallons per minute describe volume passing a point per unit time. A pressure value by itself cannot tell you the flow rate because the answer also depends on the opening size, downstream pressure, pipe losses, fluid, and geometry.

This calculator makes a specific estimate: water flows through a circular opening, and the pressure drop is converted into ideal velocity using a Bernoulli-style relationship. The calculation uses upstream pressure, exit pressure, and diameter. It returns ideal gpm, pressure drop, area, velocity, and cubic feet per second. For simple unit changes, use the pressure converter or the gallons to liters calculator. For flow units without pressure assumptions, use the flow rate calculator.

What the calculator is really estimating

The model assumes water, no elevation difference, no mechanical pump curve, no pipe friction, no fitting loss, and no discharge coefficient. It is best read as an upper-bound or comparison estimate for an opening, not as a substitute for a pipe-sizing calculation. A long hose, partially closed valve, rough pipe, small strainer, or sharp-edged orifice can reduce actual flow substantially.

The inputs should be internally consistent. If you use absolute pressure, use absolute pressure for both upstream and exit. The default example is 60 psi upstream and 14.7 psi at the exit, representing 60 psia discharging to standard atmosphere. If your gauge reads 45.3 psig and water discharges to open air, the pressure drop is the same: 45.3 psi. The calculator’s default absolute pair and that gauge interpretation produce the same ideal velocity because only the difference is used.

Formula used by the calculator

First the diameter in inches is converted to feet:

$d_{\text{ft}} = \frac{d_{\text{in}}}{12}$

Then the circular area is calculated:

$A = \pi \cdot \left(\frac{d_{\text{ft}}}{2}\right)^2$

The pressure drop is:

$\Delta P = P_1 - P_2$

The ideal water velocity used by the calculation is:

$v = \sqrt{\frac{\Delta P \cdot 32.174 \cdot 144 \cdot 2}{62.4}}$

Flow in cubic feet per second is:

$Q_{\text{cfs}} = v \cdot A$

And gallons per minute are:

$Q_{\text{gpm}} = Q_{\text{cfs}} \cdot 448.83$

The calculation uses these constants: standard gravity is 32.174 ft per second squared, water weight density is 62.4 lb per cubic foot, 144 converts square inches to square feet for pressure units, and 448.83 converts cubic feet per second to gallons per minute. Those rounded constants are common engineering approximations.

Example

Use the default values: upstream pressure 60 psi, exit pressure 14.7 psi, and opening diameter 1 inch. The pressure drop is:

$60 - 14.7 = 45.3\ \text{psi}$

The diameter in feet is 0.0833333 ft, so the circular area is:

$\pi \cdot \left(\frac{0.0833333}{2}\right)^2 \approx 0.005454\ \text{ft}^2$

The ideal velocity is:

$\sqrt{\frac{45.3 \cdot 32.174 \cdot 144 \cdot 2}{62.4}} \approx 82.02\ \text{ft/s}$

The cubic feet per second are:

$82.02 \cdot 0.005454 \approx 0.4473\ \text{ft}^3\text{/s}$

Multiplying by 448.83 gives the displayed flow:

$0.4473 \cdot 448.83 \approx 200.78\ \text{gpm}$

The result panel rounds that to about 200.78 gpm, with pressure drop 45.3 psi, pipe area 0.005454 ft squared, ideal velocity 82.02 ft per second, and flow rate 0.4473 cubic feet per second.

Reference examples

Notice how diameter dominates. Increasing diameter increases area with the square of diameter, so a slightly larger opening can move much more water at the same pressure drop. Increasing pressure raises velocity with a square root, so doubling the pressure drop does not double ideal flow.

Practical domains and pitfalls

Use this estimate for a first look at tanks, short outlets, test rigs, nozzles, and rough comparisons between opening sizes. Do not use it as the final answer for municipal service lines, irrigation zones, fire protection, long hoses, or pump selection. Those systems require friction loss, fittings, elevation, required residual pressure, and pump curves. If you need water demand rather than outlet physics, the water demand calculator may be a better starting point.

The largest pitfall is asking for psi to gpm without diameter. A second pitfall is entering 60 psig upstream and 14.7 psi exit as if both were on the same scale; that creates an inflated pressure drop. A third is using the result for gas. Water density is built into the formula, so compressed air, steam, and natural gas need different methods.

Accuracy and limits

The numerical result is only as reliable as the entered measurements and the stated physical assumptions. A unit change does not determine density, concentration, geometry, reference pressure, efficiency, or safety. Preserve extra digits during intermediate work, round only for the final use, and confirm consequential decisions against the governing label, specification, or professional method.

Sources

• Engineering ToolBox, Bernoulli Equation — pressure, velocity, and energy relationship for ideal fluid flow.
• Engineering ToolBox, Orifice, Nozzle and Venturi Flow Rate Meters — discharge concepts and real-flow corrections.
• Engineering ToolBox, Water Density, Specific Weight and Thermal Expansion — reference data for water density and specific weight.