Kinematic Viscosity of Air Calculator

Background.

Every Reynolds number computed for air — over a wing, through a duct, around a chimney — needs one property in its denominator: the kinematic viscosity ν = μ/ρ, the ratio of air's dynamic viscosity to its density. At room conditions it is about 1.57×10⁻⁵ m²/s, but it is nowhere near a constant, and this page computes it for the temperature and pressure you actually have.

The two ingredients move differently. Dynamic viscosity μ — the fluid's intrinsic stickiness — depends on temperature alone for a dilute gas and, counterintuitively, rises with heating: hotter molecules cross between flow layers faster and transfer more momentum. Sutherland's 1893 formula, μ = μ₀(T/T₀)^{3/2}(T₀+S)/(T+S) with S = 110.4 K for air, captures that rise to within about 2% from 100 to 1,900 K and remains the standard engineering correlation, used in NASA's compressible-flow references and most CFD codes.

Density brings in pressure through the ideal-gas law, ρ = p/(RT). Because ρ sits in the denominator of ν while μ ignores pressure, kinematic viscosity is strongly pressure- and altitude-dependent: halve the pressure and ν doubles. At airliner cruise altitude ν is roughly four times its sea-level value — one reason flight Reynolds numbers differ so much from wind-tunnel ones, and why tunnels are sometimes pressurised to compensate.

The model is dry, dilute air: Sutherland constants for the standard composition, ideal-gas density, no humidity correction (moist air is up to ≈1% less dense at summer conditions). For standards-grade property work there are dedicated tables; for the Reynolds numbers, settling times, and boundary-layer estimates of ordinary engineering, this correlation is the tool, and the scope note beside the result draws the line.

What is kinematic viscosity of air calculator?

Kinematic viscosity ν is dynamic viscosity divided by density, ν = μ/ρ, with units of m²/s — the diffusivity of momentum through the fluid. For air this page builds it from two standard models: Sutherland's law for μ(T), which rises with temperature as faster molecules exchange momentum between layers more effectively, and the ideal-gas law for ρ(T, p). The result is the ν that appears in the Reynolds number Re = vL/ν, in boundary-layer growth, and in Stokes settling — about 1.46×10⁻⁵ m²/s at 15 °C sea level, growing with altitude and temperature.

How to use this calculator.

1. 01Enter the absolute temperature in kelvin — °C + 273.15, so a 25 °C lab is 298.15 K.
2. 02Enter the absolute (not gauge) pressure in pascals: sea level 101,325 Pa, Denver ≈83,000 Pa, airliner cruise ≈23,000 Pa.
3. 03Read ν in m²/s; multiply by 10⁴ if a reference quotes stokes, or by 10⁶ to compare with the ‘centistokes’-scale values of oils.
4. 04Drop the result into your Reynolds number Re = vL/ν — a 0.1 m chord in a 10 m/s room-temperature stream gives Re ≈ 64,000, comfortably turbulent-transitional.
5. 05For hot or high-altitude cases, resist the temptation to reuse the sea-level 1.5×10⁻⁵: at 600 K and 1 atm ν is roughly 5×10⁻⁵ m²/s, a factor-three shift that moves flow regimes.

The formula.

The dynamic part comes from kinetic theory refined by Sutherland: an ideal hard-sphere gas would give μ ∝ √T, but real molecules attract weakly at a distance, making slow (cold) molecules act effectively larger. Sutherland modelled that with one extra constant S, giving μ = μ₀(T/T₀)^{3/2}·(T₀+S)/(T+S); for air μ₀ = 1.716×10⁻⁵ Pa·s at T₀ = 273.15 K with S = 110.4 K. Notice pressure is absent — for dilute gases, more molecules per volume also means proportionally shorter free paths, and the two effects cancel in μ. Density supplies the pressure dependence instead: ρ = p/(R_specific·T) with R = 287.05 J/(kg·K) for dry air. Dividing, ν = μRT/p: kinematic viscosity grows a little faster than T^{3/2} with temperature (both numerator effects align) and inversely with pressure. The engine evaluates the chain — Sutherland factor, gas density, quotient — in Decimal arithmetic and rounds once to twelve significant digits.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NASA Glenn Research Center, Viscosity.
2. [2]NIST Chemistry WebBook, Thermophysical Properties of Fluid Systems.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.
4. [4]NIST Special Publication 811, Guide for the Use of the International System of Units, 2008 edition.
5. [5]NASA Glenn Research Center, Equation of State.