Kinematic Viscosity of Air: Why Every Aerodynamics Problem Starts Here

At 20 °C and standard sea-level pressure (101,325 Pa), the kinematic viscosity of dry air is about 1.506 × 10⁻⁵ m²/s — equivalently 15.06 mm²/s, or 15.06 centistokes. At 300 K, the round-number condition textbooks prefer, it is 1.569 × 10⁻⁵ m²/s. Kinematic viscosity, written ν (nu), is dynamic viscosity divided by density: ν = μ/ρ. That single division is worth keeping in view, because everything people get wrong about air viscosity — including the pressure dependence most reference tables silently omit — lives inside it.

Those two values answer the search query; the rest of this guide shows where they come from. Producing them takes exactly two short calculations you can check by hand — Sutherland's law for μ, the ideal-gas relation for ρ — and understanding them explains the trap of treating ν as a temperature-only property, plus the reason ν sits in the denominator of every Reynolds number you will ever compute.

"Viscosity of air at 20 °C" means two different numbers

The bare phrase is ambiguous, and the ambiguity is nastier than it looks: because air's density is close to 1 kg/m³, the two quantities it might mean sit deceptively close in SI magnitude — a factor of about 1.2 apart — while carrying entirely different dimensions:

Dynamic viscosity measures the fluid's internal resistance to shear — how hard adjacent layers drag on each other. Kinematic viscosity normalises that drag by the fluid's inertia, which is why it, not μ, governs how flow patterns develop. Check your formula's units before picking one: anything expecting Pa·s wants μ; anything expecting m²/s wants ν.

Sutherland's law, worked by hand

The kinematic viscosity of air calculator implements one transparent quantity equation, quoting NASA Glenn's stated Sutherland constants:

ν = μ₀ (T/T₀)^(3/2) × (T₀ + S)/(T + S) × RT/p

with μ₀ = 1.716 × 10⁻⁵ Pa·s at the reference temperature T₀ = 273.15 K, Sutherland constant S = 110.4 K, and specific gas constant R = 287.058 J/(kg·K). The first two factors are Sutherland's law for dynamic viscosity; the RT/p tail converts to kinematic form through the ideal-gas density. Run it at 20 °C, which is 293.15 K:

1. Temperature ratio, raised to 3/2. 293.15 ÷ 273.15 = 1.0732, and 1.0732^1.5 = 1.1118.
2. Sutherland correction. (273.15 + 110.4) ÷ (293.15 + 110.4) = 383.55 ÷ 403.55 = 0.9504.
3. Multiply out. 1.716 × 1.1118 = 1.9078, then 1.9078 × 0.9504 = 1.8132 — so μ = 1.813 × 10⁻⁵ Pa·s. (Carry the factors unrounded and the chain lands at 1.8133 — one reason the calculator rounds only once, at the end.)

Notice the tug-of-war: the 3/2-power term grows with temperature while the Sutherland correction shrinks, and the power term wins. Warmer air is more viscous — if your intuition was trained on honey and engine oil thinning as they heat, gases run the other way.

Divide by density to get the number aerodynamics wants

The ideal-gas density at the same condition: ρ = p/(RT) = 101,325 ÷ (287.058 × 293.15) = 101,325 ÷ 84,151.1 = 1.204 kg/m³. Then:

ν = 1.813 × 10⁻⁵ ÷ 1.204 = 1.506 × 10⁻⁵ m²/s

The calculator carries this whole chain in decimal arithmetic and rounds once at the end to twelve significant digits, prints the model-scope statement beside the result, and rejects zero or negative inputs — the equation is defined for positive magnitudes only.

Dry air at 101,325 Pa, from freezing to a hot afternoon

Running the same two-step chain across everyday temperatures:

Each column is rounded independently from the full-precision chain, so dividing the rounded μ by the rounded ρ can drift in the last digit. At 0 °C both Sutherland factors equal exactly 1, so μ is the reference value itself. The 15 °C row is the standard sea-level condition — 101,325 ÷ (287.058 × 288.15) = 101,325 ÷ 82,715.8 = 1.225 kg/m³, the density you will meet again below.

The table also shows why ν is doubly temperature-sensitive. From 0 °C to 40 °C, dynamic viscosity climbs about 11% (1.907 ÷ 1.716 = 1.111) while density falls about 13% (1.127 ÷ 1.292 = 0.872). Both movements push ν the same direction, so it rises roughly 27% (1.692 ÷ 1.328 = 1.274) over a temperature span an outdoor test campaign can cross in one season.

The pressure dependence people miss

Look back at Sutherland's law: pressure appears nowhere in it. Dynamic viscosity of a dilute gas is, in this model, a function of temperature alone. But density is proportional to pressure, and ν divides by density — so kinematic viscosity is inversely proportional to pressure.

Work it at 300 K with the pressure doubled to 2 × 101,325 = 202,650 Pa. Dynamic viscosity stays 1.846 × 10⁻⁵ Pa·s. Density doubles: ρ = 202,650 ÷ (287.058 × 300) = 202,650 ÷ 86,117.4 = 2.353 kg/m³. So ν = 1.846 × 10⁻⁵ ÷ 2.353 = 0.785 × 10⁻⁵ m²/s — half the sea-level 1.569 × 10⁻⁵ (the unrounded chain halves 1.5689 to 0.7844).

This is why a kinematic viscosity quoted without its pressure is only half a statement. Reference tables listing ν against temperature are implicitly fixed at one atmosphere, and applying them to a pressurised duct, a partial-vacuum chamber, or high-altitude flight scales the answer by whatever factor the pressure differs. The same physics is a design lever: since halving ν doubles any Reynolds number at fixed speed and size, pressurising a wind tunnel buys full-scale Reynolds numbers from a small model.

Reynolds number: where the title's claim is cashed

The Reynolds number is Re = vL/ν — speed times characteristic length, divided by kinematic viscosity. It decides whether a boundary layer stays laminar or trips turbulent, how drag scales, where separation happens. And ν is its denominator, which is the literal sense in which every aerodynamics problem starts with today's topic.

A concrete case: a 0.3 m chord wing section tested at 40 m/s in 20 °C air. The numerator is 40 × 0.3 = 12 m²/s, and Re = 12 ÷ (1.506 × 10⁻⁵) ≈ 797,000. Get ν wrong by using a table row at the wrong pressure and the Reynolds number — and every conclusion resting on it — shifts by the same factor.

Reynolds number is also the hidden context behind lift data. A lift coefficient is defined by C_L = 2L/(ρv²A), and published airfoil polars report it at the Reynolds number of the measurement; comparing your case against them honestly means matching Re, which means knowing ν at your own temperature and pressure. The lift coefficient calculator recovers the coefficient from a stated force: an aircraft holding 18,000 N of lift at 70 m/s on a 16.2 m² wing in sea-level air has v² = 4,900, then 1.225 × 4,900 = 6,002.5, then 6,002.5 × 16.2 = 97,240.5, so C_L = 36,000 ÷ 97,240.5 = 0.370. Typical airfoils reach a maximum around 1.2–1.6 before stalling, so that wing cruises with margin — though at half the speed it would need four times the coefficient, about 1.48, and the margin is gone. Notice ρ working double duty across the two tools: it sits in the lift equation's denominator and inside ν itself.

Where the model stops

Everything above describes dry, dilute air treated as an ideal gas with NASA's stated Sutherland constants. Humidity, real-gas behaviour, composition changes, and rarefied conditions all fall outside that model — and the calculator prints the boundary beside its result rather than burying it in a footnote, a convention the whole Quanta collection shares. Where the stakes are standards-grade — certified test data, anything that carries a signature — the tool's citations hand you off to the NIST Chemistry WebBook, and the Sutherland result becomes a cross-check rather than the source. What the two-step chain buys you in return is a μ and a ρ you can reproduce on paper at your own temperature and pressure, before any Reynolds number built on them acquires false authority. And when a job sits close to the model's edge — humid tropical air, a near-vacuum rig, combustion temperatures — write in with the conditions: that is a property-model question best settled while it is still a lookup, not yet a design assumption.

Sources

• NASA Glenn Research Center — viscosity of air and Sutherland's formula
• NASA Glenn Research Center — the equation of state
• NIST Chemistry WebBook — thermophysical properties of fluid systems