# Prandtl Number Calculator

URL: https://speedycalculator.com/calculators/physics/prandtl-number/
Last updated: 2026-10-30

> The Prandtl number calculator finds the ratio of momentum diffusivity to thermal diffusivity of a fluid from its specific heat, dynamic viscosity and thermal conductivity, with values for common fluids.

## Inputs

- Fluid
- Specific heat c_p (J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C))
- Dynamic viscosity μ (Pa·s, mPa·s)
- Thermal conductivity k (W/(m·K), BTU/(h·ft·°F))

## Results

- Prandtl number Pr

## Formula

```
Pr = c_p·μ / k = ν / α
```

## Explanation

The Prandtl number decides whether heat or momentum spreads faster in a fluid. Liquid metals (Pr ≪ 1) conduct heat superbly; oils (Pr ≫ 1) carry momentum far more readily than heat. It is essential in convective heat-transfer correlations.

### How to use the Prandtl Number Calculator

- **Fluid**
- **Specific heat c_p**
- **Dynamic viscosity μ**
- **Thermal conductivity k**

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

### How it works

Choose a fluid or enter custom properties.

### Inputs explained

FieldWhat to enterFluidChoose one: Air (20 °C), Water (20 °C), Liquid sodium (400 °C), Methanol (20 °C) …Specific heat c_pUnits: J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C)Dynamic viscosity μUnits: Pa·s, mPa·sThermal conductivity kUnits: W/(m·K), BTU/(h·ft·°F)

### Example values

How the main result changes when **Specific heat c_p** changes and everything else stays at the example values above:

Specific heat c_p (J/(kg·K))Prandtl number Pr502.50.7137753.750.71371,0050.71371,256.250.71371,507.50.71372,0100.7137

## Worked example

Inputs — Fluid: Air (20 °C).

Results — **Prandtl number Pr = 0.71367**.

## Key terms

- **Thermal diffusivity**: k/(ρc_p), how fast heat spreads.

## FAQ

**What is the Prandtl number of air?**
About 0.71.

**Why is Pr small for liquid metals?**
They conduct heat extremely well.

**How does Pr affect boundary layers?**
High Pr gives a thermal boundary layer thinner than the velocity one.

**Does Pr depend on temperature?**
Yes, strongly for liquids such as oils.


## Sources

- [Fluid Mechanics (F. M. White) – reference text](https://www.mheducation.com/highered/product/fluid-mechanics-white-chul/M9781260258318.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)