Formula and Method for Kinematic Viscosity of Air
Kinematic viscosity (ν) is a fluid's dynamic (absolute) viscosity divided by its density: ν = μ / ρ, with SI units of m²/s. It describes how quickly momentum diffuses through a fluid under its own inertia, and it is the quantity that appears directly in the Reynolds number, Re = VL/ν, which governs whether a flow is laminar or turbulent. Because both the dynamic viscosity of air and its density change with temperature — and density also changes with pressure — kinematic viscosity is not a single fixed number; it must be computed for the actual temperature and pressure of the air in question.
How the calculation works
This calculator first converts your temperature to kelvin, then finds air's dynamic viscosity μ using Sutherland's law: μ = μ₀ × (T₀+C)/(T+C) × (T/T₀)^1.5, where μ₀ = 1.716×10⁻⁵ Pa·s is the reference viscosity at T₀ = 273.15 K and C = 110.4 K is Sutherland's constant for air. Next it finds air density ρ from the ideal gas law, ρ = P / (R·T), using the specific gas constant for dry air, R = 287.058 J/(kg·K), and your chosen pressure. Finally it divides: ν = μ / ρ, reported in both m²/s and centistokes (1 cSt = 10⁻⁶ m²/s = 1 mm²/s).
Where kinematic viscosity of air matters
- Reynolds number and flow regime: HVAC duct design, aerodynamics, and pipe-flow calculations all use ν to determine Re = VL/ν and predict laminar versus turbulent flow.
- Altitude and weather effects: because density falls faster than viscosity as pressure drops, kinematic viscosity actually increases at altitude even though dynamic viscosity barely changes — this affects aircraft boundary-layer and fan performance calculations.
- Heat transfer and boundary layers: ν appears in the Prandtl and Grashof numbers used to size heat exchangers, cooling fans, and natural-convection systems.
Common mistakes
- Mixing up μ and ν: dynamic viscosity (Pa·s) and kinematic viscosity (m²/s) are different quantities with different units — always check which one a downstream formula expects.
- Using a Celsius or Fahrenheit value inside Sutherland's law: the formula requires absolute temperature in kelvin; plugging in °C or °F directly gives a badly wrong viscosity.
- Ignoring pressure at altitude: using sea-level air density for a high-altitude or high-pressure calculation understates or overstates ν — always match the pressure to the actual conditions.
- Confusing m²/s and cSt: kinematic viscosity is often tabulated in centistokes (mm²/s); forgetting the 10⁶ conversion factor produces a result a million times too small or too large.