# Kinematic Viscosity of Air Calculator

Created by Joanna Śmietańska, PhD candidate
Reviewed by Steven Wooding
Last updated: Dec 21, 2022

Table of contents:

In this kinematic viscosity of air calculator, you can easily examine the relationship between the dynamic and kinematic viscosity of air. Viscosity is an important property of fluids and gases, especially if you consider aerodynamic problems. Both viscosity terms are interconnected. For example, you can determine the kinematic viscosity of air if the dynamic viscosity and density are already known.

In this calculator, we will learn more about viscosity, with a particular focus on the kinematic and dynamic viscosity of air. Keep reading to learn:

• What does viscosity mean?
• How to calculate the kinematic and dynamic viscosity of air?
• What does the viscosity of air depend on?
• What is the viscosity of air at 20 degrees Celsius? What is the viscosity of air at sea level?

## What does viscosity mean?

Imagine an object moving in slow motion through the air. Aerodynamic forces are created between the air and the object because the air molecules near the object will become disturbed and move around the object. The magnitude of these forces depends on the object's shape and velocity, the gas's mass, and two other important properties of the air: viscosity and compressibility.

When an object moves in a gas, the gas molecules stuck to its surface form moving surfaces between which friction is created. Viscosity tells us how much resistance air has to flow and how resistant it is to gradual deformation under stress. We can distinguish two types of viscosity: dynamic and kinematic viscosity of the air.

💡 We are using the same terms to describe viscosity both in air and liquids because air and all other gasses can be considered fluids. Their molecules are in constant motion, and they flow as in liquids.

## Dynamic viscosity of air

A dynamic viscosity (or absolute viscosity) is generated if we have different surfaces of air molecules moving parallel to the object's surface. This results in a shear force. To overcome the resistance of the fluid, an external force $F$ must be applied per unit of moving surface. The magnitude of $F$ is proportional to the speed $v$ and the area $A$ of the moving surface and inversely proportional to their separation $y$:

$F = \mu A\frac{v}{y}$

The dynamic viscosity $μ$ (Greek letter mu) is the proportionality coefficient in this formula, and we can express it in SI units: μ = kg/m·s = N/m² = Pa·s. In practice, we can use the following empirical formula for engineering purposes:

$\mu = \frac{1.458\times 10^{-6}\times T^{\frac{3}{2}}}{T+110.4},$

where:

• $1.458×10^{-6}$ – Constant;
• $T$ – Temperature; and
• $110.4$ – Another empirical constant.

## Kinematic viscosity of air

Kinematic viscosity (marked with the Greek letter nu $\nu$) describes a relationship between dynamic (absolute) viscosity and air density. For comparison, check water viscosity calculator. You can obtain the kinematic viscosity of air by dividing dynamic viscosity by the density $\rho$:

$\nu = \frac{\mu}{\rho}$

In the SI system, the unit of kinematic viscosity is m2/s, but other commonly used units are Stokes (St): 1 St = 10-4 m2/s = 1 cm2/s. Since 1 Stoke is a large unit, it is convenient to divide it by 100 to obtain smaller unit centiStokes (cSt):

• 1 St = 100 cSt;
• 1 cSt = 10-6 m2/s = 1 mm2/s; and
• 1 m2/s = 106 centiStokes

You can estimate the density of air $\rho$ at a given pressure and temperature directly from the ideal gas law equation:

$\rho = \frac{P}{RT},$

where:

• $P$ – Absolute pressure;
• $R$ – Specific gas constant, which equals 287.05 J/(kg·K); and
• $T$ – Absolute temperature.

## How to use kinematic viscosity of air calculator?

To calculate the dynamic and kinematic viscosity of air at chosen conditions, you need to follow only a few steps:

1. Determine the pressure P. If you want to convert different units, try our pressure conversion tool.

2. Determine the temperature T.

3. Calculate the air density ρ and dynamic and kinematic viscosity using the formulas above.

Congratulations to you for working on our kinematic viscosity of air calculator.

## FAQ

### What does the viscosity of air depend on?

In general, the viscosity of air is only slightly dependent on the pressure but is strongly related to temperature.

The dynamic viscosity directly correlates with the square root of temperature μ ∝ √T, and density is inversely proportional to temperature: ρ ∝ 1/T. Therefore, we can relate these two proportionalities and derive the relationship between kinematic viscosity and temperature as ν = T3/2.

As you can see now, when the temperature rises, the viscosity of the air increases. This distinguishes air and most gases from the viscosity of liquids. For liquids, viscosity generally decreases as temperature increases.

### What is the viscosity of air at 20 degrees Celsius?

The kinematic viscosity of air at 20 degrees Celsius and 1 atm (101,325 Pa, sea level) pressure is approximately 1.51×10-5 m2/s or 15.20 cSt. The dynamic viscosity of air at sea level under the same temperature is 1.81×10-5 Pa·s. Here are the values of the kinematic and dynamic viscosity of air at a constant pressure of 1 atm and different temperatures:

Temperature (°C)

Density (kg/m3)

Dynamic viscosity (Pa·s)

Kinematic viscosity (m2/s)

-10

1.341

1.666×10-5

1.242×10-5

0

1.292

1.716×10-5

1.328×10-5

10

1.246

1.765×10-5

1.456×10-5

20

1.204

1.813×10-5

1.506×10-5

30

1.164

1.861×10-5

1.598×10-5

40

1.127

1.908×10-5

1.692×10-5

50

1.092

1.954×10-5

1.788×10-5

### How do I calculate the kinematic viscosity at 1 bar and 50 °C?

To calculate the kinematic viscosity of air at pressure 1 bar (105 Pa) and 50 °C, enter a few details into the kinematic viscosity of air calculator:

1. Convert the temperature in Celsius to kelvin: T = 273.15 K + 50 = 323.15 K.

2. Calculate the density of the air from the ideal gas law:

ρ = P/(RT) = 105 Pa/(287.05 J/kg·K × 323.15 K) = 1.078 kg/m3

3. Calculate the dynamic viscosity at given conditions:

μ = (1.458×10-6 × 323.15 K3/2)/(323.15 K + 110.4) = 1.95×10-5 Pa·s.

4. Calculate the kinematic viscosity:

ν = 1.95×10-5Pa·s / 1.078 kg/m3 = 1.81×10-5 m2/s.

### How can I convert kinematic viscosity to dynamic viscosity?

You can easily convert between the dynamic and kinematic viscosity of air as both quantities are related by the equation ν = μ/ρ.

For example, if the density of air ρ is equal to 1.113 kg/m3 and ν = 1.697×10-5 m2/s, you can modify the equation above to obtain μ = ν×ρ = 1.697×10-5 m2/s × 1.113 kg/m3 = 1.889×10-5 Pa·s.

Joanna Śmietańska, PhD candidate
Pressure (P)
Pa
Temperature (T)
K
Specific gas constant (Rₛ)
J/(kg·K)
Density (ρ)
kg/m³
Dynamic viscosity (μ)
Pa⋅s
Kinematic viscosity (ν)
m²/s
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