Free PSI to GPM Calculator

What the PSI to GPM Calculator Does

The PSI to GPM calculator is an online tool that converts pressure readings in pounds per square inch (PSI) into a water flow rate expressed in gallons per minute (GPM) or gallons per hour. By applying Bernoulli’s principle for an ideal fluid, this flow rate calculator helps plumbers, engineers, and DIY users estimate the discharge rate through a pipe when only the pressure at two points and the pipe diameter are known.

The Difference Between PSI and GPM

PSI (pounds per square inch) is a pressure unit — it measures the force exerted per unit area. One PSI equals about 6894.76 pascals. It is commonly seen on tire gauges, pressure washers, and municipal water systems. GPM (gallons per minute), on the other hand, quantifies the volume of fluid moving through a system per minute. One US GPM is approximately $6.309 \times 10^{-5}\ \text{m}^3/\text{s}$. Although they are not directly convertible (pressure vs. flow rate), they are linked through the fluid’s velocity and the pipe’s geometry.

Bernoulli’s Equation at Constant Height

For an incompressible, frictionless fluid flowing without elevation change, Bernoulli’s equation simplifies to:

$$P_1 + \frac{1}{2} \rho v_1^{2} = P_2 + \frac{1}{2} \rho v_2^{2}$$

where $\rho$ is the fluid density (water ≈ $62.4\ \text{lb/ft}^3$) and $v$ is the flow velocity. If the upstream kinetic energy is negligible (e.g., large tank feeding a small pipe, $v_1 \approx 0$), the equation reduces to:

$$\Delta P = P_1 - P_2 = \frac{1}{2} \rho v_2^{2}$$

Solving for velocity:

$$v_2 = \sqrt{\frac{2 \Delta P}{\rho}}$$

From Velocity to Flow Rate

The volumetric flow rate $Q$ is the product of the velocity and the pipe’s cross‑sectional area $A$:

$$Q = v_2 \times A$$

The area for a circular pipe is $A = \pi \left( \frac{d}{2} \right)^{2}$, where $d$ is the inner diameter. With $v_2$ in ft/s and $A$ in ft², $Q$ comes out in ft³/s. To obtain GPM, multiply by $448.83$ — the number of US gallons in one cubic foot times 60 seconds per minute: $7.4805 \times 60 \approx 448.83$.

Illustrative Example

Assume a water tank is pressurized to 80.0 PSI and discharges to the open air (14.7 PSI) through a 2‑inch‑diameter pipe. The pressure difference is $\Delta P = 80.0 - 14.7 = 65.3\ \text{PSI}$.

1. Convert ΔP to lb/ft² – multiply by 144: $65.3 \times 144 = 9403.2\ \text{lb/ft}^2$.
2. Find velocity – $v = \sqrt{ \frac{2 \times 9403.2}{62.4} } = \sqrt{301.4} \approx 17.36\ \text{ft/s}$.
3. Pipe area – radius $1\ \text{in} = 0.08333\ \text{ft}$, $A = \pi (0.08333)^2 \approx 0.02182\ \text{ft}^2$.
4. Flow rate (ft³/s) – $Q = 17.36 \times 0.02182 \approx 0.3787\ \text{ft}^3/\text{s}$.
5. Convert to GPM – $0.3787 \times 448.83 \approx 170.0\ \text{GPM}$.

Thus, under ideal conditions, the pipe delivers roughly 170 gallons per minute. An actual system would yield slightly less due to friction losses.

Using the Online PSI to GPM Converter

With the calculator, you do not have to work through the algebra and unit conversions manually. Simply enter:

• Internal pressure (PSI)
• External or outlet pressure (PSI), typically atmospheric
• Pipe diameter (inches) or directly the cross‑sectional area

The tool instantly returns the flow rate in GPM or gallons per hour. It handles the conversion of PSI to lb/ft², applies Bernoulli’s equation, and performs the area and unit calculations. This makes it an essential water flow calculator for quick estimates on the job or for educational purposes.

Assumptions and Limitations

The derived flow rate is a theoretical maximum because Bernoulli’s equation assumes:

• Incompressible, frictionless fluid — real water has viscosity, and pipes have roughness that causes head loss.
• Steady flow and no turbulence.
• Constant elevation — the pipe inlet and outlet are at the same height.
• Negligible inlet velocity — valid when the tank cross‑section is much larger than the pipe.

For engineering designs, corrections using the Darcy‑Weisbach or Hazen‑Williams formulas are recommended. Nevertheless, the PSI to GPM calculator provides a valuable first‑pass estimate for any pipe‑flow scenario.