Psi to Liters per Minute? Direct Conversion

Psi and liters per minute measure two different things: psi (pounds per square inch) is a unit of pressure, while liters per minute (L/min) is a unit of flow rate. You cannot convert psi to L/min directly because flow also depends on the pipe or hose size, its length, and the fluid’s properties. This calculator converts a pressure drop (in psi) across a circular pipe into an estimated flow rate in liters per minute, using the Darcy–Weisbach equation with water at room temperature.

Formula

The calculator uses the Hagen–Poiseuille equation for laminar flow through a straight, circular pipe:

Q = (ΔP × π × r⁴) / (8 × μ × L)

• Q = volumetric flow rate (m³/s)
• ΔP = pressure drop (pascals, Pa)
• r = pipe inner radius (meters, m)
• μ = dynamic viscosity of water (Pa·s, about 0.001 at 20°C)
• L = pipe length (meters, m)

To convert psi to pascals, multiply by 6894.76. To convert m³/s to L/min, multiply by 60,000. The calculator does both conversions automatically.

Worked Example

Using the default values: pipe diameter = 15 mm (0.015 m), length = 10 m, pressure drop = 20 psi.

1. Convert pressure: 20 psi × 6894.76 = 137,895.2 Pa
2. Radius = 0.015 / 2 = 0.0075 m
3. r⁴ = (0.0075)⁴ = 3.164 × 10⁻⁹ m⁴
4. Plug into the equation: Q = (137,895.2 × π × 3.164×10⁻⁹) / (8 × 0.001 × 10)
5. Numerator = 137,895.2 × 3.14159 × 3.164×10⁻⁹ = 1.370 × 10⁻³
6. Denominator = 8 × 0.001 × 10 = 0.08
7. Q = 1.370 × 10⁻³ / 0.08 = 0.01713 m³/s
8. Convert to L/min: 0.01713 × 60,000 = 1,027.8 L/min

The calculator shows 1,027.8 L/min, matching the step-by-step result.

Why Direct Conversion Is Impossible

Pressure and flow are related, but not interchangeable. Think of water in a garden hose: with the same faucet pressure, a wide hose delivers far more liters per minute than a narrow one. The relationship is governed by resistance—narrower pipes, longer runs, and bends all reduce flow. The Hagen–Poiseuille equation captures this for smooth, straight pipes with laminar flow (Reynolds number below about 2300). Most practical water flows in household pipes are turbulent, so this formula gives a theoretical maximum; actual flow will be lower.

How to Use the Calculator

Measure the pipe’s inner diameter (not the outer thread size) in millimeters. For a typical 1/2-inch PVC pipe, the inner diameter is about 15 mm; for 3/4-inch, it’s about 20 mm. Enter the length of the pipe in meters and the pressure drop in psi—this is the pressure difference between the inlet and outlet, not the static line pressure. If you have a pump, use the pump’s head pressure minus the outlet pressure. The result is the maximum flow rate for smooth, straight pipe with water at 20°C.

Common Mistakes and Misconceptions

• Using outer diameter instead of inner: A 15 mm outer pipe may have a 12 mm bore, which reduces flow by over 50%.
• Confusing pressure drop with system pressure: A 50 psi water main does not mean a 50 psi drop across your hose—the drop is the difference between the two ends.
• Ignoring turbulence: The formula assumes smooth laminar flow. Real flows are often turbulent, so actual flow is lower than calculated.
• Forgetting fittings and bends: Each elbow or valve adds resistance, effectively lengthening the pipe.

When This Formula Applies

Use this calculator for short, straight, smooth pipes carrying water or similar low-viscosity fluids. It works well for drip irrigation lines, laboratory tubing, and small hydraulic systems. It does not apply to gases (compressible), very viscous fluids, or pipes with significant elevation changes. For turbulent flow, you’d need the Darcy–Weisbach equation with a friction factor, which is more complex.

Frequently Asked Questions

Can I convert psi to L/min for a garden hose?

Only if you know the hose’s inner diameter and length. A 25-meter, 13 mm garden hose with 40 psi drop might deliver about 30 L/min, but the actual value depends on fittings and whether the hose is coiled or straight.

What is the difference between psi and bar?

Bar is another pressure unit. 1 bar = 14.5038 psi. To convert psi to bar, divide by 14.5038. Many European pumps list pressure in bar, so you may need to convert before using this calculator.

Why does my pump’s flow rate differ from the calculator?

Pumps have performance curves—they deliver lower flow at higher pressure. The calculator assumes a fixed pressure drop, but a pump’s actual pressure drop depends on the system resistance, so you may need to iterate: guess a flow, find the pump’s pressure at that flow, then recalculate.

Does water temperature matter?

Yes. Hot water has lower viscosity, so it flows faster at the same pressure. At 60°C, water’s viscosity is about 0.00047 Pa·s, roughly half that at 20°C, which would roughly double the flow rate in the formula.

Can I use this for air or other gases?

No. Gases are compressible, so their density changes with pressure, and the Hagen–Poiseuille equation assumes incompressible flow. For air, you’d need a different formula that accounts for expansion.

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in d | Pipe inner diameter | mm | 15 | 0
in l | Pipe length | m | 10 | 0
in dp | Pressure drop | psi | 20 | 0
out flow | Flow rate | L/min | (dp*6894.76*3.14159*(d/1000)^4)/(128*0.001*(l)) * 60000 | 2
out vel | Velocity | m/s | (flow/60000)/(3.14159*(d/1000)^2/4) | 2