Compute the kinematic viscosity of dry air ν = μ/ρ from temperature and pressure. Dynamic viscosity μ(T) uses the Sutherland formula; density ρ(T,P) uses the ideal-gas law. Results in m²/s, cSt (mm²/s) and ft²/s, with intermediate μ and ρ shown.
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Kinematic viscosity ν (m²/s)
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ν in cSt (= mm²/s)
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ν in ft²/s
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Dynamic viscosity μ (Pa·s)
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Density ρ (kg/m³)
Reference table: ν vs temperature at 1 atm (101.325 kPa)
Computed with the same Sutherland + ideal-gas model. Values rounded for display; the calculator uses full precision.
T (°C)
ν (10⁻⁶ m²/s)
ν (cSt)
μ (10⁻⁶ Pa·s)
ρ (kg/m³)
-20
11.5849
11.58
16.1533
1.3943
-10
12.4214
12.42
16.6615
1.3414
0
13.2798
13.28
17.1608
1.2922
10
14.1596
14.16
17.6515
1.2466
20
15.0605
15.06
18.1341
1.2041
30
15.9818
15.98
18.6087
1.1644
40
16.9234
16.92
19.0757
1.1272
50
17.8847
17.88
19.5355
1.0923
60
18.8655
18.87
19.9882
1.0595
70
19.8653
19.87
20.4342
1.0286
80
20.8839
20.88
20.8737
0.9995
90
21.9210
21.92
21.3069
0.9720
100
22.9762
22.98
21.7341
0.9459
Spot-check vs measured data (Engineering ToolBox, 1 atm): 0°C → 13.30 cSt measured vs 13.28 computed; 40°C → 16.97 vs 16.92; 100°C → 23.06 vs 22.98 (all within 0.4%).
How it is calculated
μ = 1.458×10⁻⁶ · T3/2 / (T + 110.4) [Pa·s, T in K] ρ = P / (287.058 · T) [kg/m³, dry air] ν = μ / ρ [m²/s]
Sutherland constants for air: S = 110.4 K. The form above gives μ = 17.16×10⁻⁶ Pa·s at 273.15 K, matching measured viscosity data (Engineering ToolBox: 17.10×10⁻⁶ at 0°C). Dynamic viscosity of a gas is essentially independent of pressure up to several MPa, so pressure enters only through density: at fixed temperature, ν is inversely proportional to pressure (halving the pressure doubles ν).
Valid range: roughly −50°C to +300°C and pressures up to ~3.5 MPa. Humid air is slightly less dense than dry air at the same T and P; this calculator models dry air.
Related tools
Density alone (without viscosity)? See the air density calculator (#391). Using ν in pipe-flow head loss? See the Darcy-Weisbach calculator (#409), which uses the Reynolds number Re = vD/ν.
Frequently asked questions
What is the kinematic viscosity of air?
Kinematic viscosity, denoted ν (nu), is the ratio of a fluid's dynamic viscosity μ to its density ρ: ν = μ/ρ. For air it measures how quickly momentum diffuses through the gas, and it appears in the Reynolds number (Re = vD/ν). Its SI unit is m²/s; 1 m²/s = 10⁶ cSt.
What is the kinematic viscosity of air at 20°C?
At 20°C and standard atmospheric pressure (101.325 kPa), the kinematic viscosity of dry air is 15.06×10⁻⁶ m²/s, i.e. 15.06 cSt (equivalently 15.06 mm²/s). This is the value this calculator produces for its default inputs.
How is the kinematic viscosity of air calculated?
In two steps. First, dynamic viscosity μ(T) from the Sutherland formula μ = 1.458×10⁻⁶ · T^1.5 / (T + 110.4) with T in kelvin. Second, density ρ = P/(287.058·T) from the ideal-gas law with P in pascal. Then ν = μ/ρ. This calculator follows exactly this procedure.
What are the Sutherland constants for air?
The Sutherland constant S for air is 110.4 K. In the form μ = C·T^1.5/(T+S) the constant C = 1.458×10⁻⁶ kg/(m·s·K^0.5), which gives μ = 17.16×10⁻⁶ Pa·s at 273.15 K, matching measured viscosity tables (Engineering ToolBox lists 17.10×10⁻⁶ Pa·s at 0°C).
Does pressure affect the kinematic viscosity of air?
Dynamic viscosity μ is essentially independent of pressure (up to a few MPa), but density ρ is proportional to pressure, so kinematic viscosity ν = μ/ρ is inversely proportional to pressure at fixed temperature. Halving the pressure doubles ν: at 20°C and 50.6625 kPa the value is 30.12 cSt versus 15.06 cSt at 101.325 kPa.
Why does the kinematic viscosity of air increase with temperature?
In gases, viscosity comes from molecules colliding and exchanging momentum; hotter molecules move faster and collide more often, so μ rises with temperature. Density falls with temperature, and both effects push ν = μ/ρ upward: from 13.28 cSt at 0°C to 22.98 cSt at 100°C (1 atm).
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity μ (Pa·s) measures internal friction and appears in shear-stress relations. Kinematic viscosity ν = μ/ρ (m²/s) divides out density, so it governs how fast viscous effects diffuse. Convert with ν = μ/ρ: e.g. μ = 18.13×10⁻⁶ Pa·s and ρ = 1.2041 kg/m³ at 20°C give ν = 15.06×10⁻⁶ m²/s.
What units are used for kinematic viscosity?
SI: m²/s. Common engineering units: cSt (centistokes) = mm²/s (1 m²/s = 10⁶ cSt), Stokes (1 St = 10⁻⁴ m²/s), and ft²/s in imperial work (1 m²/s = 10.7639 ft²/s). This calculator reports all three.
How accurate is this calculator?
Within its range (about -50°C to 300°C, up to ~3.5 MPa) the Sutherland model matches measured air-viscosity tables to better than 0.5%: computed 13.28 cSt vs measured 13.30 cSt at 0°C, 16.92 vs 16.97 at 40°C, and 22.98 vs 23.06 at 100°C (1 atm, Engineering ToolBox). It models dry air; humid air is slightly less dense.
Where is the kinematic viscosity of air used?
Anywhere airflow is analyzed: the Reynolds number Re = vD/ν sets the laminar/turbulent regime in ducts and pipes, aerodynamic drag and boundary layers scale with ν, and HVAC duct sizing, fan selection, and wind-tunnel testing all use it. Related: the air density calculator for ρ alone, and the Darcy-Weisbach calculator for pipe head loss using Re.
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