Idealized water flow estimate

PSI to GPM Calculator

Estimate water flow through a circular opening from upstream-to-downstream pressure difference and opening diameter.

Pressure and opening

Enter pressures and diameter

psi + in → US GPM

Upstream pressure (psi)

Downstream pressure (psi)

Opening diameter (inches)

Estimated discharge

Flow rate

The estimated flow will appear here

Enter both pressures on the same basis and an opening diameter in inches.

What is PSI to GPM?

The PSI to GPM Calculator estimates water discharge through an idealized circular opening from pressure difference and diameter. It uses a compact orifice-style relation with a fixed coefficient and assumes water has specific gravity 1. The result is gallons per minute.

Pressure by itself does not determine flow through a real pipe network. Length, internal roughness, fittings, valves, elevation, viscosity and opening geometry all create losses. Use this result as a quick scenario for the stated equation, not as a pump-sizing result or a guarantee of delivered flow.

How to Use This Calculator

Enter pressure inside the tank in pounds per square inch and pressure at the exit in the same unit.
Enter the opening diameter in inches. The page requires a positive diameter and treats it as the diameter used directly in its circular-opening relation.
Choose Calculate. The page subtracts exit pressure from inside pressure, takes the square root of that pressure difference, multiplies by diameter squared and then by 29.84.
Read the result in U.S. gallons per minute. The pressure inside must be at least the exit pressure; otherwise the assumed forward-flow direction does not apply.
For equipment decisions, compare the estimate with a manufacturer curve or a hydraulic calculation that includes the actual line and discharge coefficient.

Formula Used

GPM = 29.84 × d² × √(ΔP/SG), where ΔP = Pinside − Pexit in psi, d is diameter in inches, and this page fixes specific gravity SG at 1 for water.

Variables Explained

Term	Meaning	Assumption on this page
Pinside	Upstream tank pressure in psi.	Measured on the same pressure basis as exit pressure.
Pexit	Downstream or exit pressure in psi.	Cannot exceed upstream pressure for this forward-flow estimate.
ΔP	Pressure difference that drives the estimate.	Losses elsewhere are not separately entered.
d	Opening diameter in inches.	Positive and used as d².
SG	Fluid specific gravity relative to water.	Fixed at 1; other liquids are outside this form.
GPM	Estimated U.S. gallons per minute.	Rounded to two decimal places.

Worked Example

With 9 psi inside, 5 psi at the exit and a 1-inch diameter, ΔP = 9 − 5 = 4 psi. The estimate is 29.84 × 1² × √4 = 29.84 × 2 = 59.68 GPM.

If diameter doubles while pressure difference stays at 4 psi, the d² term makes the estimate four times as large. If pressure difference quadruples while diameter stays fixed, the square-root term makes the estimate twice as large.

Why Use This Calculator?

A zero pressure difference returns zero flow in this idealized relation. A negative difference is rejected because it would imply reverse flow and the square root would not be real under the entered direction.

The 29.84 factor packages unit conversions and a particular discharge assumption. The U.S. Bureau of Reclamation explains that theoretical orifice flow must be corrected for contraction and real-fluid effects, and that a discharge coefficient depends on geometry and installation. A pipe outlet, nozzle and sharp-edged opening do not necessarily share one coefficient.

For a long pipe, use a line-loss method and include elevation and components. For a nozzle or valve, use tested flow coefficients or manufacturer data. Measured flow under operating conditions is the best check when safety, supply or equipment performance depends on the answer.

Pressure readings should describe the operating condition of interest. Static pressure with every outlet closed can be quite different from pressure while water is moving, so combining a static reading with a desired operating flow may overstate what the installation can deliver.

Common Mistakes

Entering absolute upstream pressure and gauge downstream pressure in the same calculation.
Using millimetres for a field that expects inches.
Entering pipe radius instead of diameter.
Trying to calculate forward flow when exit pressure is higher.
Applying the water result to a liquid with a different specific gravity.
Ignoring pipe length, elbows, valves and surface roughness.
Treating a two-decimal display as measured accuracy.

Frequently Asked Questions

Does PSI convert directly to GPM?

No. Flow also needs an opening size and assumptions about the fluid and restrictions. This page uses diameter and a fixed water-based relation.

Should I enter gauge or absolute pressure?

Use the same basis for both pressures. Their difference drives the formula, so consistent gauge readings commonly work for this comparison.

What happens when both pressures are equal?

The pressure difference is zero, so this idealized equation returns zero GPM.

Can exit pressure be greater than tank pressure?

Not for the forward-flow calculation shown. That condition suggests reverse flow or another driving source and is rejected.

Can I use this for oil?

Not without changing the fluid assumption. The page fixes specific gravity at 1, and viscosity can add effects that this relation does not describe.

Why does diameter have such a large effect?

The formula uses diameter squared because opening area grows with the square of diameter. Small diameter measurement errors can therefore noticeably change the estimate.

Is this suitable for pump selection?

Use a full system curve and the pump manufacturer’s performance data. This simple result omits the losses and operating conditions needed for selection.