What this calculator does
Kinematic viscosity measures how readily a fluid flows under its own inertia: it is the dynamic viscosity divided by density, and it turns up directly in the Reynolds number that tells you whether a flow of air is laminar or turbulent. Air's kinematic viscosity is not a single fixed number the way it is sometimes quoted in a textbook table, because it changes with both temperature and pressure.
This calculator works out both figures properly rather than looking one up. Dynamic viscosity comes from Sutherland's formula, a well-established empirical fit for how a gas's viscosity rises with temperature. Density comes from the ideal gas law, using the entered pressure and temperature. Dividing one by the other gives the kinematic viscosity at your exact conditions, not just at sea level and room temperature.
The formula
Sutherland's formula gives the dynamic viscosity μ from absolute temperature T, using a reference viscosity μ₀ = 1.716×10⁻⁵ Pa·s at T₀ = 273.15 K and Sutherland's constant S = 110.4 K for air. Air density ρ then comes from the ideal gas law using the specific gas constant for dry air, R = 287.05 J/(kg·K). Kinematic viscosity ν is simply μ divided by ρ.
| Term | Meaning |
|---|---|
| μ (mu) | Dynamic viscosity, in pascal-seconds: the fluid's resistance to shearing, independent of density. |
| ν (nu) | Kinematic viscosity, in square metres per second: dynamic viscosity divided by density. |
| ρ (rho) | Air density at the entered temperature and pressure, from the ideal gas law. |
| cSt | Centistokes, 1 mm²/s: the everyday unit kinematic viscosity is usually quoted in. |
The inputs explained
| Field | What to enter |
|---|---|
| Air temperature (°C) | The air temperature at the point you care about, in degrees Celsius. |
| Absolute pressure (kPa) | The absolute pressure of the air, in kilopascals. Standard sea-level pressure is 101.325 kPa; at altitude, or in a pressurised or evacuated system, use the actual figure. |
When to use it
Reynolds number and duct sizing
HVAC and fan calculations need the Reynolds number to check whether airflow through a duct will be laminar or turbulent, and that calculation needs kinematic viscosity, not the dynamic figure most reference tables quote.
Working at altitude or in a pressurised system
A fixed kinematic viscosity of air quoted for sea level understates the true value at altitude, where lower pressure means lower density and a higher ν for the same dynamic viscosity.
Comparing hot and cold air handling
Furnace flues, drying processes and cold-store ventilation all move air well away from room temperature, where viscosity has shifted enough from the textbook 15°C figure to matter in a flow calculation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How kinematic viscosity of air changes with temperature
The same pressure, across a range of temperatures from well below freezing to well above room temperature.
| Temperature | Kinematic viscosity | Dynamic viscosity |
|---|---|---|
| -20°C | 11.58 mm²/s (cSt) | 16.153 µPa·s |
| 0°C | 13.28 mm²/s (cSt) | 17.160 µPa·s |
| 15°C | 14.61 mm²/s (cSt) | 17.893 µPa·s |
| 25°C | 15.52 mm²/s (cSt) | 18.371 µPa·s |
| 40°C | 16.92 mm²/s (cSt) | 19.075 µPa·s |
| 100°C | 22.97 mm²/s (cSt) | 21.733 µPa·s |
How kinematic viscosity of air changes with pressure
The same temperature, at pressures from sea level down to roughly the pressure at high altitude.
| Pressure | Kinematic viscosity |
|---|---|
| 101.325 kPa | 14.61 mm²/s (cSt) |
| 90 kPa | 16.44 mm²/s (cSt) |
| 80 kPa | 18.50 mm²/s (cSt) |
| 70 kPa | 21.14 mm²/s (cSt) |
| 60 kPa | 24.67 mm²/s (cSt) |
| 50 kPa | 29.60 mm²/s (cSt) |
Questions
What is the kinematic viscosity equation?
Kinematic viscosity ν equals dynamic viscosity μ divided by density ρ. This calculator gets μ from Sutherland's formula, a standard fit for how a gas's dynamic viscosity rises with temperature, and ρ from the ideal gas law at the entered pressure and temperature.
Why does kinematic viscosity depend on pressure if dynamic viscosity does not?
Dynamic viscosity of a gas depends mainly on temperature, not pressure, over the ranges most engineering work covers. But kinematic viscosity divides by density, and density is directly proportional to pressure, so a change in pressure alone changes the kinematic figure even though the dynamic one barely moves.
What is a typical kinematic viscosity of air at room temperature?
At 15°C and standard atmospheric pressure, air's kinematic viscosity works out to about 14.6 mm²/s (14.6 centistokes). It rises with temperature and falls as pressure or density increases.
How is this different from the viscosity of water?
Air and water are governed by completely different physics: air's viscosity comes from momentum transfer between molecules and rises with temperature, while a liquid like water gets less viscous as it warms. They need different reference data and different formulas.
For the equivalent figures in water rather than air, see the water viscosity calculator. For flow through a pipe once you have a viscosity figure, see Poiseuille's law.