# PSI to GPM Calculator (Pressure to Flow Rate)

URL: https://speedycalculator.com/calculators/conversion/psi-to-gpm/
Last updated: 2026-10-25

> The PSI to GPM calculator estimates the water flow rate from a tank, hose or pipe outlet from the pressure difference and the opening’s diameter, using Bernoulli’s equation with a discharge coefficient.

## Inputs

- Pressure inside (psi, kPa, bar)
- Pressure at the exit (psi, kPa, bar)
- Opening diameter (in, cm, mm)
- Discharge coefficient

## Results

- Flow rate
- Exit velocity

## Formula

```
Q = C_d × A × √(2 × ΔP ÷ ρ)
```

## Explanation

Pressure pushes water out of an opening at a speed set by Bernoulli’s principle; the flow rate is that speed times the opening area. Real outlets lose energy to friction and contraction, captured by the discharge coefficient C_d (about 0.97 for a smooth nozzle, 0.6 for a sharp-edged hole).

### How to use the PSI to GPM Calculator

- **Pressure inside**
- **Pressure at the exit**
- **Opening diameter**
- **Discharge coefficient**
- Every result field is editable: type into **Flow rate** and **Pressure inside** plus every other field update to match.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The pressure difference is converted to pascals, the ideal outlet velocity is found from √(2ΔP/ρ) with water’s density, and it is multiplied by the opening area and C_d.

### Inputs explained

FieldWhat to enterPressure insideUnits: psi, kPa, barPressure at the exitUnits: psi, kPa, barOpening diameterUnits: in, cm, mmDischarge coefficientA number

### What each result means

- **Flow rate** = [Discharge coefficient] × pi × [Opening diameter]^2 ÷ 4 × sqrt(2 × max([Pressure inside] - [Pressure at the exit], 0) ÷ 998.2)
- **Exit velocity** = sqrt(2 × max([Pressure inside] - [Pressure at the exit], 0) ÷ 998.2)

### Example values

How the main result changes when **Pressure inside** changes and everything else stays at the example values above:

Pressure inside (psi)Flow rate (GPM)3039.6494548.566056.0727562.6919068.67412079.298

## Worked example

Inputs — Pressure inside: 60 psi; Pressure at the exit: 0 psi; Opening diameter: 0.5 in; Discharge coefficient: 0.97.

Results — **Flow rate = 56.072 GPM**; Exit velocity = 94.46 ft/s.

## FAQ

**How many GPM through a 1/2″ opening at 60 psi?**
About 22 GPM in theory; hoses and fittings reduce this.

**Does this include pipe friction?**
No. Long pipes lose pressure; use a pipe-friction calculator for those.

**What formula does the PSI to GPM Calculator use?**
Q = C_d × A × √(2 × ΔP ÷ ρ).


## Sources

- [NIST Special Publication 811 – Guide for the Use of the International System of Units](https://www.nist.gov/pml/special-publication-811)
- [NIST Handbook 44 Appendix C – General tables of units of measurement](https://www.nist.gov/pml/owm/nist-handbook-44-current-edition)