Kinematic Viscosity of Air Calculator
Find the kinematic viscosity (ν = μ/ρ) of air at a given temperature and pressure. Uses Sutherland's law for dynamic viscosity and the ideal-gas law for density — the standard approach in fluid mechanics and aerodynamics.
°C
kPa
(= centistokes, cSt) — Sutherland's law + ideal-gas density
- 1
Temperature in kelvin
20 + 273.15 = 293.15 K - 2
Sutherland factor
(293.15 ÷ 273.15)^(3/2) × (383.55 ÷ 403.55) = 1.056715Combined temperature-ratio and Sutherland correction for molecular collision frequency. - 3
Dynamic viscosity μ
1.716×10⁻⁵ × 1.056715 = 1.8133e-5 Pa·s - 4
Air density ρ = P ÷ (R × T)
101,325 ÷ (287.058 × 293.15) = 1.2041 kg/m³ - 5
Kinematic viscosity ν = μ ÷ ρ × 10⁶
1.8133e-5 ÷ 1.2041 × 10⁶ = 15.0598
How does this calculator work?
Kinematic viscosity of air ν = μ/ρ, where dynamic viscosity μ comes from Sutherland's law (≈1.458×10⁻⁶×T^(1.5)/(T+110.4)) and density ρ = P/(287.058×T) from the ideal-gas law. At 20°C and 101.325 kPa, ν ≈ 1.516×10⁻⁵ m²/s. Viscosity rises with temperature; kinematic viscosity falls with pressure.
Formula
How this is calculated
Kinematic viscosity ν (nu) is defined as dynamic viscosity μ divided by density ρ. For air, the dynamic viscosity at any temperature is calculated via Sutherland's empirical law: μ = μ_ref × (T/T_ref)^(3/2) × (T_ref + S)/(T + S), where T is absolute temperature in kelvin, T_ref = 273.15 K, μ_ref = 1.716×10⁻⁵ Pa·s, and S = 110.4 K (Sutherland's constant for air). This formula is accurate to within about 2% for temperatures from −50°C to 1000°C.
Density is found from the ideal-gas law ρ = P/(R_air × T), where P is absolute pressure in pascals and R_air = 287.058 J/(kg·K) is the specific gas constant for dry air. Together these give ν = μ/ρ in m²/s. Results are also shown in mm²/s, which equals centistokes (cSt).
This approach is standard for dry air. It does not account for humidity (moist air has slightly lower density), trace gases, or highly elevated pressures where the ideal-gas assumption breaks down. At standard sea-level conditions (20°C, 101.325 kPa) the kinematic viscosity is approximately 1.516×10⁻⁵ m²/s (15.16 mm²/s).
Frequently asked questions
Dynamic viscosity μ (Pa·s) measures the internal friction of a fluid. Kinematic viscosity ν (m²/s) is μ divided by density — it captures how freely a fluid flows under its own weight and is the quantity that appears in the Reynolds number and many flow equations.
Unlike liquids, gases become more viscous as temperature rises because higher kinetic energy increases molecular collisions that transfer momentum across flow layers. This is captured by the T^(3/2) term in Sutherland's law.
Pressure has almost no effect on dynamic viscosity (μ), but it directly increases density. Higher pressure means denser air, so kinematic viscosity ν = μ/ρ decreases with increasing pressure.
Also known as
TG we-Calculate Editorial Team. (2026). Kinematic Viscosity of Air Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/kinematic-viscosity-of-air-calculator
TG we-Calculate Editorial Team. "Kinematic Viscosity of Air Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/kinematic-viscosity-of-air-calculator.
TG we-Calculate Editorial Team, "Kinematic Viscosity of Air Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/kinematic-viscosity-of-air-calculator
@misc{wecalculate_kinematic_viscosity_of_air_calculator, title = {Kinematic Viscosity of Air Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/kinematic-viscosity-of-air-calculator}}, year = {2026}, note = {TG we-Calculate} }
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