Calculate air dynamic and kinematic viscosity from temperature and pressure using Sutherland’s law, with density, cP, cSt, and Reynolds number results.
Viscosity of Air Formula
The calculator uses Sutherland’s formula for dynamic viscosity, then derives kinematic viscosity and Reynolds number from it.
μ = (1.458 ×10⁻⁶ × T(3/2)) / (T +110.4)
ν = μ / ρ, where ρ = P / (R × T)
- μ = dynamic viscosity (Pa·s)
- ν = kinematic viscosity (m²/s)
- T = absolute temperature (K)
- P = positive absolute pressure (Pa); the example uses101325Pa
- ρ = air density (kg/m³)
- R = specific gas constant for air = 287.05 J/(kg·K)
- V = flow velocity (m/s)
- L = characteristic length (m)
Sutherland’s formula is an empirical dry-air dilute-gas estimate. Density here uses the ideal-gas law. The retained100–1900K input range is not a universal1%accuracy guarantee. The model treats dynamic viscosity as temperature-dependent only and includes no pressure, humidity, dense-gas, phase-change or rarefied-flow correction. Density and kinematic viscosity depend on the entered positive absolute pressure; accepting an input does not validate those physical assumptions.
Reference Values
Use these values to spot-check inputs or to estimate without running the calculator.
| Temp (°C) | μ (Pa·s) | ν at 1 atm (m²/s) | ρ at 1 atm (kg/m³) |
|---|---|---|---|
| -20 | 1.62×10⁻⁵ | 1.16×10⁻⁵ | 1.394 |
| 0 | 1.72×10⁻⁵ | 1.33×10⁻⁵ | 1.292 |
| 20 | 1.81×10⁻⁵ | 1.51×10⁻⁵ | 1.204 |
| 40 | 1.91×10⁻⁵ | 1.69×10⁻⁵ | 1.127 |
| 100 | 2.17×10⁻⁵ | 2.30×10⁻⁵ | 0.946 |
| 200 | 2.57×10⁻⁵ | 3.45×10⁻⁵ | 0.746 |
| 500 | 3.55×10⁻⁵ | 7.77×10⁻⁵ | 0.457 |
| Reynolds Number | Flow Regime (internal pipe flow) |
|---|---|
| Re < 2300 | Laminar |
| 2300 – 4000 | Transitional |
| Re > 4000 | Turbulent |
Example
Find the dynamic and kinematic viscosity of air at 25°C and 1 atm.
- Convert: T = 25 + 273.15 = 298.15 K
- μ = (1.458×10⁻⁶ × 298.151.5) / (298.15 + 110.4) = 1.837×10⁻⁵ Pa·s
- ρ = 101325 / (287.05 × 298.15) = 1.184 kg/m³
- ν = μ / ρ = 1.552×10⁻⁵ m²/s
FAQ
Does humidity affect air viscosity? Humidity is not included in this dry-air model. Use an appropriate humid-air property model when composition effects matter; no humidity error bound is claimed here.
Why does viscosity rise with temperature? In gases, higher temperature means faster molecular motion and more momentum transfer between layers, which increases viscosity. Many liquids instead become less viscous as temperature rises.
Does pressure change dynamic viscosity? This dilute-gas model ignores pressure dependence of dynamic viscosity. Kinematic viscosity changes through density. Dense-gas conditions can require a more complete property model; no universal10atm accuracy threshold is claimed here.
What characteristic length should I use for Reynolds number? Pipe diameter for internal flow, chord length for an airfoil, and the dimension parallel to flow for a flat plate.
