Kinematic Viscosity of Air Calculator
Enter the air temperature and absolute pressure to get the kinematic viscosity instantly. The calculator applies Sutherland's law for dynamic viscosity and the ideal gas law for air density, then divides one by the other. All three intermediate values are shown so you can see exactly how the result is built up. Switch between SI and US customary units; results update as you type.
Formula
Worked example
At 20 °C (293.15 K) and 101,325 Pa: mu = (1.458e-6 × 293.15^1.5) / (293.15 + 110.4) = 1.813e-5 Pa·s. rho = 101325 / (287.05 × 293.15) = 1.204 kg/m³. nu = 1.813e-5 / 1.204 = 1.506e-5 m²/s (15.06 cSt).
What is kinematic viscosity?
Kinematic viscosity (symbol nu, Greek letter nu) is a measure of how readily a fluid flows under gravity. It is defined as the ratio of dynamic viscosity to density: nu = mu / rho. The SI unit is m²/s, but engineers often use the centistoke (cSt), which equals 10^-6 m²/s. Because density changes with pressure and temperature, kinematic viscosity captures both the fluid's internal resistance to shear and its inertia in one number. For air, kinematic viscosity rises with temperature because Sutherland's law predicts a stronger increase in dynamic viscosity than the ideal gas law predicts in density.
How kinematic viscosity of air is calculated
This calculator uses two well-established models. First, Sutherland's law gives dynamic viscosity as a function of temperature alone: mu = (C1 × T^1.5) / (T + S), where C1 = 1.458 × 10^-6 kg/(m·s·K^0.5) and S = 110.4 K is Sutherland's constant for air. Second, the ideal gas law gives air density: rho = P / (Rs × T), where Rs = 287.05 J/(kg·K) is the specific gas constant for dry air and P is absolute pressure in pascals. Dividing dynamic viscosity by density gives kinematic viscosity. At 20 °C and 1 atm the result is about 1.51 × 10^-5 m²/s, matching standard reference tables to within 1%.
Effect of temperature and pressure on nu
Temperature has a much stronger effect on kinematic viscosity than pressure does. As temperature rises, dynamic viscosity increases (following Sutherland's power law), while density decreases. Both effects push kinematic viscosity higher, so nu roughly doubles between 0 °C and 200 °C. Pressure has only an indirect effect: higher pressure increases air density without changing dynamic viscosity (Sutherland's law is pressure-independent for ideal gases), so kinematic viscosity decreases in proportion to the pressure ratio. At sea level (1 atm) and 20 °C, nu is about 1.51 × 10^-5 m²/s; at 0.5 atm (roughly 5,500 m altitude) it doubles to about 3.0 × 10^-5 m²/s.
Engineering applications and the Reynolds number
Kinematic viscosity is central to the Reynolds number Re = V × L / nu, where V is flow velocity and L is a characteristic length (pipe diameter, chord length, body width). Re determines whether a flow is laminar (low Re, smooth layers) or turbulent (high Re, chaotic mixing), with a critical value near 2,300 for pipe flow and 5 × 10^5 for flat-plate boundary layers. Aerospace engineers use nu at altitude (lower pressure, varied temperature) to compute Re over a wing and decide whether to expect laminar or turbulent boundary layers. HVAC designers use it to size ducts and predict heat transfer coefficients. Because nu depends on temperature and pressure, always use the actual conditions of the application, not a room-temperature default.
Kinematic viscosity of air at standard pressure (101,325 Pa)
| Temperature (°C) | nu (m²/s) | nu (× 10⁻⁶ m²/s) | mu (Pa·s) | rho (kg/m³) |
|---|---|---|---|---|
| -50 | 9.42e-6 | 9.42 | 1.474e-5 | 1.563 |
| -25 | 1.12e-5 | 11.2 | 1.596e-5 | 1.423 |
| 0 | 1.33e-5 | 13.3 | 1.716e-5 | 1.293 |
| 15 | 1.46e-5 | 14.6 | 1.789e-5 | 1.225 |
| 20 | 1.52e-5 | 15.2 | 1.813e-5 | 1.204 |
| 25 | 1.56e-5 | 15.6 | 1.837e-5 | 1.184 |
| 50 | 1.80e-5 | 18.0 | 1.963e-5 | 1.093 |
| 100 | 2.31e-5 | 23.1 | 2.182e-5 | 0.946 |
| 200 | 3.49e-5 | 34.9 | 2.577e-5 | 0.746 |
| 300 | 5.01e-5 | 50.1 | 2.934e-5 | 0.616 |
| 400 | 6.73e-5 | 67.3 | 3.265e-5 | 0.525 |
| 500 | 8.60e-5 | 86.0 | 3.571e-5 | 0.458 |
Computed with Sutherland's law and the ideal gas law. Values in m²/s × 10⁻⁶.
Frequently asked questions
What is the kinematic viscosity of air at room temperature?
At 20 °C (68 °F) and standard atmospheric pressure (101,325 Pa), the kinematic viscosity of air is approximately 1.51 × 10^-5 m²/s, or about 15.1 cSt. This value is widely used as the default in aerodynamic and HVAC calculations.
Why does kinematic viscosity increase with temperature for air?
As temperature rises, the dynamic viscosity of air increases (gas molecules collide more vigorously, transferring more momentum), while the density decreases (the gas expands). Since kinematic viscosity is dynamic viscosity divided by density, both effects push it upward. This is the opposite of liquids, where kinematic viscosity typically falls with temperature.
How does altitude affect the kinematic viscosity of air?
Altitude reduces pressure, which lowers air density. Since Sutherland's law does not depend on pressure, dynamic viscosity stays roughly the same, and kinematic viscosity (= mu / rho) rises in proportion to the pressure drop. At cruising altitude (about 12 km, pressure around 20,000 Pa), kinematic viscosity is roughly five times higher than at sea level at the same temperature.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity (mu, Pa·s) measures a fluid's internal resistance to shear deformation regardless of its density. Kinematic viscosity (nu, m²/s) is dynamic viscosity divided by density; it represents how quickly momentum diffuses through the fluid under its own weight. When comparing fluids or computing Reynolds numbers, kinematic viscosity is usually more convenient because it accounts for density automatically.
Is Sutherland's law accurate at very high or very low temperatures?
Sutherland's law is accurate for dry air between about -50 °C and 1000 °C, typically within 1-2%. At very high temperatures (above 1500 °C), dissociation and ionization effects mean the formula loses accuracy, and more complex models are required. At cryogenic temperatures below about -100 °C, deviations from ideal behaviour also grow. For ordinary engineering and atmospheric applications the formula is highly reliable.
What units should I use for the Reynolds number calculation?
Plug kinematic viscosity in m²/s into Re = V × L / nu, with V in m/s and L in m. The result is dimensionless. If you work in US customary units, use nu in ft²/s, V in ft/s, and L in ft. Never mix unit systems: kinematic viscosity in cSt with lengths in cm would require an additional conversion factor.