The air viscosity calculator above derives viscosity rather than converting it. You give it a temperature, and it evaluates Sutherland's law to produce the dynamic viscosity of dry air. It then works out the air density at your pressure and divides one by the other to give the kinematic viscosity, which is the version that appears in the Reynolds number and in almost every other piece of dimensionless fluid analysis.
Arb Digital publishes a viscosity converter as well, and the two do genuinely different jobs. That tool takes a viscosity you already know and rescales it between poise, pascal-seconds, stokes and the rest; it computes nothing about the fluid. This page does the opposite: it produces a viscosity from the state of the air, and never asks you for one.
What This Air Viscosity Calculator Does
Viscosity is a fluid's resistance to shear. Dynamic viscosity, usually written μ, is the constant of proportionality between shear stress and velocity gradient, and its SI unit is the pascal-second. Kinematic viscosity, written ν, is that divided by density, and its unit is the square metre per second. The two describe the same physical property but answer different questions, and using the wrong one is the single most common error in this corner of fluid mechanics.
For air the dynamic viscosity depends on temperature and essentially not at all on pressure, over any range you are likely to meet outside a compressor or a vacuum chamber. That is a genuinely surprising result and it goes back to the kinetic theory of gases. Kinematic viscosity, however, depends strongly on pressure, because density does. That is why the tool asks for both numbers even though only one of them touches μ.
The grid reports the kinematic viscosity in SI and in centistokes, the dynamic viscosity in centipoise, and the density that was used to link them. Centipoise and centistokes survive in industry because water at room temperature is conveniently close to one of each, so the CGS units give numbers people can hold in their head.
How to Use It
- Enter the air temperature. It is the only input that changes the dynamic viscosity, and the relationship is not linear, so a rough estimate is not good enough at high temperatures.
- Set the absolute pressure. This affects only the density and therefore the kinematic viscosity. Use absolute pressure, not gauge, or the density will be wrong by an atmosphere.
- Override the density if you have a better figure. Humid air is slightly less dense than dry air at the same conditions, and if that matters you should supply the density yourself.
- Set a comparison temperature. The sentence under the grid then tells you how much the viscosity has changed between the two, which is the fastest way to see whether temperature control matters for your problem.
- Take the kinematic value into a Reynolds number. That is what most people need this for, and the Reynolds number calculator is the next step.
The Formula: How Air Viscosity Is Calculated
The tool uses Sutherland's law, an empirical relation built on a simple model of molecules as attracting rigid spheres. In SI form it is μ = μ0 × (T ÷ T0)1.5 × (T0 + S) ÷ (T + S), with the reference viscosity μ0 = 1.716 × 10−5 Pa·s at T0 = 273.15 K and a Sutherland constant S of 110.4 K for air. All temperatures are absolute.
NASA Glenn Research Center's page on viscosity gives the same relation in imperial units, with a Sutherland constant of 198.72 degrees Rankine, which is exactly 110.4 kelvin restated. That page also makes the point this calculator is built on: viscosity depends on temperature and stays effectively constant as pressure changes.
Density comes from the ideal gas law, ρ = PM ÷ (RT), with the molar mass of dry air taken as 0.0289647 kg/mol and the universal gas constant as 8.314463 J/(mol·K). Kinematic viscosity is then simply ν = μ ÷ ρ. If you need a defensible measured value rather than a correlation, the NIST Chemistry WebBook thermophysical properties of fluid systems serves tabulated viscosity for air and many other working fluids at a state you specify.
Work the defaults by hand. At 20 °C, T = 293.15 K. The ratio T ÷ T0 is 1.073220, and raised to the power 1.5 that is 1.111814. The Sutherland factor is (273.15 + 110.4) ÷ (293.15 + 110.4) = 383.55 ÷ 403.55 = 0.950440. Multiplying gives μ = 1.716 × 10−5 × 1.111814 × 0.950440 = 1.8133 × 10−5 Pa·s. Density at 101,325 Pa is 101,325 × 0.0289647 ÷ (8.314463 × 293.15) = 2,934.83 ÷ 2,437.38 = 1.2041 kg/m³, so ν = 1.8133 × 10−5 ÷ 1.2041 = 1.506 × 10−5 m²/s, or 15.06 centistokes.
Why Heating Air Makes It Thicker
Everyone has warmed honey to make it pour. Gases do the reverse, and the reason is that viscosity in a gas has nothing to do with molecules sticking together. It comes from momentum transport. Molecules wander sideways across a shear layer, carrying the velocity of the layer they came from into the layer they arrive in, and that exchange is what resists the shear.
Heat the gas and the molecules move faster, so they cross the shear layer more often and carry more momentum with them. The resistance goes up. In a liquid, by contrast, the molecules are packed close enough that viscosity comes mostly from intermolecular attraction, and heating loosens that grip. Two completely different mechanisms, two opposite temperature trends.
The scale of it surprises people. Air at 500 °C is roughly twice as viscous as air at 20 °C. Any calculation involving hot gas — a flue, an oven, a turbine, a combustion chamber — that quietly uses a room-temperature viscosity is wrong by a factor that matters, and the error goes the wrong way from intuition.
Why Pressure Does Not Change Dynamic Viscosity
Kinetic theory gives dynamic viscosity as roughly one third of the density times the mean molecular speed times the mean free path. Double the pressure and you double the density, but you halve the mean free path, because molecules are packed twice as tightly and collide twice as soon. The two changes cancel exactly, and μ stays put.
This holds well from near-vacuum up to many atmospheres. It breaks down at very high densities, where molecules spend a significant fraction of their time within range of each other and the gas starts behaving a little like a liquid, and it breaks down at very low pressures, where the mean free path grows to the size of the apparatus and continuum viscosity stops being a meaningful idea at all.
Kinematic viscosity behaves completely differently, and this is the part that catches out aerodynamicists. At 11 kilometres the air is about four times less dense than at sea level and colder, so μ falls a little but ν rises by roughly a factor of three and a half. Higher kinematic viscosity means a lower Reynolds number for the same aircraft at the same speed, which is precisely why wind tunnel work has to worry about Reynolds matching rather than just speed matching.
Which Viscosity Your Formula Wants
The rule is simple once you have seen it. If the formula also contains a density, it almost certainly wants dynamic viscosity. If it does not, it almost certainly wants kinematic. Shear stress in Newton's law of viscosity uses μ. The Reynolds number is written both ways, as ρvL ÷ μ or as vL ÷ ν, and the two are identical.
Stokes' law for a sphere settling through a fluid uses dynamic viscosity, and the Stokes' law calculator handles that case. Pressure drop along a pipe through the Darcy-Weisbach route needs a friction factor that depends on the Reynolds number, so the friction factor calculator takes it from there. Whichever route you take, get the viscosity at the working temperature rather than at the temperature of the room the equipment sits in.
Units are the other trap. A centipoise is 0.001 Pa·s and a centistoke is 10−6 m²/s, and air's dynamic viscosity of about 0.018 cP against its kinematic viscosity of about 15 cSt is a ratio of nearly a thousand between two numbers that are both called viscosity. If you have a figure whose units you are unsure of, run it through the viscosity converter before it reaches a formula.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using a room-temperature viscosity for hot gas — air roughly doubles in viscosity between 20 °C and 500 °C, and the change is in the opposite direction to liquid intuition.
- Mixing up dynamic and kinematic — they differ by the density, which for air is close to 1.2, so the numbers are not obviously wrong. Check whether your formula already contains a density.
- Entering gauge pressure — the ideal gas law needs absolute pressure. Feeding it a gauge reading understates the density by an atmosphere and inflates the kinematic viscosity accordingly.
- Using Celsius in Sutherland's law — every temperature in the relation is absolute. Substituting Celsius produces a plausible-looking number that is simply wrong.
- Extrapolating far outside the fit — Sutherland's law is a correlation, not a law of nature. Below about 100 K and above about 1,900 K it should not be trusted, and near dissociation it fails completely.
Related Free Tools From Arb Digital
Take the kinematic viscosity straight into the Reynolds number calculator, then on to the friction factor calculator for pipe losses. The Stokes' law calculator covers settling and drag on small spheres using the dynamic value. For the air state itself, the air density calculator handles humid air properly and the speed of sound calculator covers the other big temperature-driven air property. Use the viscosity converter for units, the temperature converter for inputs, and the pressure converter if your pressure is in bar or psi. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
At 20 degrees Celsius the dynamic viscosity of dry air is about 1.81 times ten to the minus five pascal-seconds. At standard sea-level pressure the density is about 1.204 kilograms per cubic metre, so the kinematic viscosity works out at roughly 1.51 times ten to the minus five square metres per second, or 15.1 centistokes.
More viscous. Gases behave the opposite way to liquids because their viscosity comes from molecules carrying momentum across the flow rather than from attraction between them. Faster molecules cross more often, so the resistance to shear rises with temperature.
It does not affect dynamic viscosity to any useful degree over ordinary ranges, because raising pressure increases density and shortens the mean free path by matching amounts that cancel. It strongly affects kinematic viscosity, which is dynamic viscosity divided by density.
An empirical relation that gives gas viscosity as a function of absolute temperature, using a reference viscosity, a reference temperature and a gas-specific Sutherland constant. For air that constant is 110.4 kelvin, and the fit is dependable from roughly 100 kelvin to 1,900 kelvin.
Dynamic viscosity relates shear stress to velocity gradient and is measured in pascal-seconds. Kinematic viscosity is that value divided by density and is measured in square metres per second. If a formula already contains a density it almost always wants the dynamic value.
Because density falls much faster with altitude than dynamic viscosity does. At eleven kilometres the air is roughly four times thinner, so even though the cold reduces the dynamic viscosity a little, dividing by a much smaller density raises the kinematic value substantially.
Only slightly. Water vapour has a lower viscosity than dry air, so moist air is marginally less viscous, and it is also less dense. The effect is small compared with temperature, but you can enter a measured humid-air density in the override box if it matters to you.
This tool is provided for educational and study use. Sutherland's law is an empirical correlation for dry air and the density comes from ideal gas behaviour, so the output is a physics estimate rather than a measured or certified property value; take design-grade figures from a reference database or from your own measurements.
