Kinematic Viscosity Of Air Calculator - Air Property At Temperature

The kinematic viscosity of air is the ratio of its dynamic (absolute) viscosity to its mass density. It tells you how easily air flows and spreads momentum once you set aside the pull of gravity, and it is written as nu = mu / rho. Because both mu and rho shift with temperature and pressure, the value is not one fixed number but something you compute for the exact conditions of your problem.

• • Duct and fan design: Engineers size ventilation and HVAC ducts using the air property that sets the Reynolds number for the flow.
• • Aerodynamics: Students studying lift and drag on wings need the property that appears inside the dimensionless flow numbers.
• • Heat transfer: Forced-convection correlations for air moving over a surface call for this property to predict how heat travels with the flow.

In practice you meet this quantity whenever air moves through a pipe, around a body, or through a porous medium. It decides whether a flow stays laminar or turns turbulent, and it enters the Nusselt and Stanton numbers used in convection work. If you are modelling a room, a fan, or a small vehicle, this is the property that links your geometry and speed to the flow regime.

Most published tables quote air in centistokes (cSt), where 1 cSt equals 1e-6 m^2/s. Our calculator reports the kinematic viscosity of air in both the SI unit and centistokes, and it also returns the dynamic viscosity and the air density, because density is the term that connects the result to pressure. When you need only the mass density for a separate step, the air density calculator gives that value directly for the same inputs.

The calculator builds the result from two physical laws. First it finds the dynamic viscosity of air at your temperature with Sutherland's law, then it finds the air density from the ideal gas law, and finally it divides the two.

• mu0: Reference dynamic viscosity of air, 1.716e-5 Pa*s at T0 = 273.15 K.
• S: Sutherland constant for air, 110.4 K; it captures how viscosity grows with temperature.
• R: Specific gas constant for dry air, 287.05 J/(kg*K), used in the density term.

Worked example: at 20 C and 101.325 kPa the dynamic viscosity is about 1.813e-5 Pa*s and the density is about 1.204 kg/m^3, so the kinematic viscosity of air is 1.506e-5 m^2/s, or 15.06 cSt. That matches the published air viscosity table at Engineering Toolbox, which lists roughly 15.16 cSt at 20 C and one atmosphere. The small gap is rounding in the reference constants.

Notice that the kinematic viscosity of air rises faster with temperature than dynamic viscosity does. Dynamic viscosity grows mildly because warmer molecules exchange momentum more readily, but density falls as the gas expands, and that fall dominates the quotient. Feed the same fluid properties into the Reynolds number calculator and it returns whether a flow is laminar, transitional, or turbulent.

The Engineering Toolbox - Air: Absolute and Kinematic Viscosity table lists roughly 15.16 cSt at 20 C and one atmosphere, matching this Sutherland plus ideal-gas result to within rounding.

The Wikipedia - Viscosity page explains the underlying viscosity definitions and the Sutherland relationship in detail.

Feed the same fluid properties into the Reynolds number calculator and it returns whether a flow is laminar, transitional, or turbulent for your conditions.

Three related ideas show up whenever you use air viscosity in a calculation.

Density is the bridge from pressure to the result. Two air samples at the same temperature but different pressures have the same dynamic viscosity yet different kinematic viscosities, because the denser (higher-pressure) sample gives a smaller quotient. Keep this in mind when you compare sea-level and altitude conditions.

The poise-stokes converter switches between CGS units (poise, stokes) and the SI units used here, which is handy when a textbook quotes air properties in stokes.

Follow these steps to get a value you can trust.

1. 1 Enter temperature: Type the air temperature in degrees Celsius. If you have a Kelvin value, subtract 273.15 first, since the calculator adds 273.15 back internally.
2. 2 Enter pressure: Type the pressure in kilopascals. Use 101.325 kPa for standard sea level, or read local pressure from a barometer for your altitude.
3. 3 Read the results: The primary result is the kinematic viscosity in m^2/s, with centistokes, dynamic viscosity in Pa*s, and density in kg/m^3 shown alongside.
4. 4 Apply in your model: Feed nu into the Reynolds number with your velocity and length, or compare it against a published table.

Example: a lab at 25 C and 100 kPa. Enter 25 and 100, and the kinematic viscosity comes out near 1.56e-5 m^2/s (15.6 cSt), close to the sea-level value because the pressure is only slightly below one atmosphere. For a gas mixture at the same T and P, the gas density calculator estimates density for comparison.

For a gas mixture at the same temperature and pressure, the gas density calculator estimates density for comparison against the air value reported here.

Using the calculator instead of a printed table gives a few concrete advantages.

• • Any condition: The Sutherland plus ideal-gas model gives a smooth value from -100 C to 1000 C and any pressure in range, not just the rows a table prints.
• • Two units at once: You get m^2/s and centistokes in one step, so you can drop the number into an SI Reynolds number or compare it against a textbook table.
• • Density shown: Seeing density and dynamic viscosity next to the answer makes it obvious why the value changed when you adjusted pressure rather than temperature.
• • Altitude and vacuum: Change the pressure input to model altitude or a vacuum chamber instead of assuming a fixed sea-level constant.
• • Fewer unit slips: Temperature in Celsius and pressure in kPa are handled for you, including the Kelvin shift and the Pa conversion.

Because the model is continuous, you can also probe conditions that tables rarely list, such as the thin air at cruising altitude or a pressurised wind tunnel, and still get a consistent number tied to the same physics.

Two inputs and one assumption drive the number you see.

• • Sutherland's law fits air well between about -100 C and 1000 C but is empirical, not an exact equation of state, so do not treat the output as a metrology-grade standard.
• • The ideal gas law also loses accuracy at very high pressures, which the 1000 kPa upper limit avoids, and it should not be used near phase-change conditions.

The Engineering Toolbox - Dry Air Properties reference tabulates the properties of dry air, including viscosity limits across a temperature range, which is a useful check before you apply a value in a design calculation.

The Prandtl number calculator shows why air sits near a Prandtl number of 0.7 across a wide temperature range, since both momentum and thermal diffusivities scale with temperature.