Calculate kinematic viscosity ν, dynamic viscosity μ, and density of air at any temperature and pressure using Sutherland's law.
Kinematic viscosity ν = μ/ρ is one of the most important fluid properties in engineering. It appears in the Reynolds number (Re = VD/ν), boundary-layer equations, and virtually every convection heat-transfer correlation. For air, both dynamic viscosity μ and density ρ depend on temperature and pressure, so ν varies significantly across conditions.
This calculator uses Sutherland's law to compute the dynamic viscosity of air as a function of temperature, combined with the ideal gas law for density. Sutherland's formula — μ = μ₀ (T/T₀)^(3/2) (T₀+C)/(T+C) with C ≈ 120 K — is accurate to within 2% from −40°C to 1 500°C. Density is calculated from ρ = PM/(RT), with optional humidity correction.
The temperature-sweep table provides a complete reference from −40°C to 500°C, letting you look up viscosity at any condition without needing a textbook. A bar chart visualises how ν increases sharply with temperature — roughly doubling between 0°C and 200°C.
Use this calculator when Reynolds number, boundary-layer behavior, or convective heat transfer depends on realistic air properties instead of a single handbook value.
It is useful for CFD setup, duct and wind-speed calculations, altitude work, and quick engineering checks where temperature and pressure move away from standard conditions. That makes it easier to keep downstream flow calculations consistent with the actual operating state instead of a default ambient assumption.
Sutherland's Law: μ = μ₀ × (T₀ + C)/(T + C) × (T/T₀)^(3/2) μ₀ = 1.827 × 10⁻⁵ Pa·s, T₀ = 291.15 K, C = 120 K Density (ideal gas): ρ = PM / (RT) M = 0.02896 kg/mol, R = 8.314 J/(mol·K) Kinematic viscosity: ν = μ / ρ
Result: ν = 15.16 × 10⁻⁶ m²/s
μ = 1.825 × 10⁻⁵ Pa·s from Sutherland. ρ = 101325 × 0.02896 / (8.314 × 293.15) = 1.204 kg/m³. ν = 1.825×10⁻⁵ / 1.204 = 1.516×10⁻⁵ m²/s.
Air viscosity matters most when it feeds another calculation such as Reynolds number, pressure loss, or heat-transfer coefficient. Under standard indoor conditions a memorized value may be good enough, but once temperature, altitude, or process gas conditions move away from ambient, property changes become large enough to affect the answer materially.
The most common mistake is mixing dynamic viscosity and kinematic viscosity. Another is using standard-density air at reduced pressure, which can shift Reynolds number and flow regime more than expected. If humidity is important, remember that its effect is usually secondary compared with temperature and pressure.
Dynamic viscosity of gases increases with temperature (more molecular momentum transfer), while density decreases. Both effects increase ν = μ/ρ, making the rise quite steep — roughly proportional to T^1.7.
Dynamic viscosity of an ideal gas is nearly independent of pressure. However, density is proportional to pressure, so kinematic viscosity ν = μ/ρ is inversely proportional to pressure.
Within about 2% for temperatures from −40°C to 1 500°C at moderate pressures. At very high pressures (> 100 atm) or near the critical point, real-gas corrections are needed.
At 20°C and 1 atm, ν ≈ 1.51 × 10⁻⁵ m²/s. This is about 15 times the kinematic viscosity of water, which is ~1.0 × 10⁻⁶ m²/s.
Humid air is slightly less dense than dry air (water vapor is lighter than N₂/O₂). This increases kinematic viscosity slightly but the effect is usually small (< 2% at 60% RH).
At higher altitudes, pressure drops and ν increases. A higher ν means Re = VD/ν is lower for the same velocity and length, potentially delaying the transition to turbulence or reducing heat-transfer coefficients.