# Poiseuille’s Law Calculator

URL: https://speedycalculator.com/calculators/physics/poiseuilles-law/
Last updated: 2026-10-30

> The Poiseuille's law calculator finds the volumetric flow of a viscous fluid through a narrow tube in laminar flow from the pressure difference, the tube radius and length and the fluid viscosity – plus the flow resistance.

## Inputs

- Dynamic viscosity μ (mPa·s (cP), Pa·s)
- Tube radius r (mm, cm, m, in, µm)
- Tube length L (cm, mm, m, in, ft)
- Pressure difference ΔP (Pa, kPa, mmHg, bar)

## Results

- Flow rate Q
- Flow resistance
- Mean velocity

## Formula

```
Q = π·r⁴·ΔP / (8·μ·L),  R = 8μL/(πr⁴)
```

## Explanation

In laminar flow through a pipe the flow rate rises with the fourth power of the radius. Narrowing an artery by 20% cuts blood flow by almost 60% at the same pressure – which is why atherosclerosis is so dangerous.

### How to use the Poiseuille's Law Calculator

- **Dynamic viscosity μ**
- **Tube radius r**
- **Tube length L**
- **Pressure difference ΔP**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the viscosity, tube radius, length and pressure difference.

### Inputs explained

FieldWhat to enterDynamic viscosity μUnits: mPa·s (cP), Pa·sTube radius rUnits: mm, cm, m, in, µmTube length LUnits: cm, mm, m, in, ftPressure difference ΔPUnits: Pa, kPa, mmHg, bar

### What each result means

- **Flow rate Q** = pi×[Tube radius r]^4×[Pressure difference ΔP]÷(8×[Dynamic viscosity μ]×[Tube length L])
- **Flow resistance** = 8×[Dynamic viscosity μ]×[Tube length L]÷(pi×[Tube radius r]^4)
- **Mean velocity** = [Tube radius r]^2×[Pressure difference ΔP]÷(8×[Dynamic viscosity μ]×[Tube length L])

### Example values

How the main result changes when **Dynamic viscosity μ** changes and everything else stays at the example values above:

Dynamic viscosity μ (mPa·s (cP))Flow rate Q (mL/s)1.753.59042.632.39363.51.79524.381.43625.251.196870.8976

## Worked example

Inputs — Dynamic viscosity μ: 3.5 mPa·s (cP); Tube radius r: 2 mm; Tube length L: 10 cm; Pressure difference ΔP: 100 Pa.

Results — **Flow rate Q = 1.7952 mL/s**; Flow resistance = 55,704,230.08216 Pa·s/m³; Mean velocity = 14.28571 cm/s.

## Key terms

- **Laminar flow**: Smooth, layered flow without mixing.

## FAQ

**Why the fourth power of r?**
Both area and velocity grow with r².

**When is the law valid?**
Laminar, steady flow of a Newtonian fluid in a long rigid tube.

**Does it apply to blood?**
Approximately – blood is non-Newtonian and vessels are elastic.

**What is the maximum velocity?**
Twice the mean, at the centre.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)