Kinematic vs dynamic viscosity: what's the difference and when to use each

The Reynolds number formula calls for "kinematic viscosity," but many fluid data sheets list only "dynamic viscosity" (or the reverse). Viscosity notation is a common source of confusion in fluid mechanics. This article explains the difference.

The simple explanation

Think of viscosity as "fluid thickness." Honey is thick, meaning high viscosity. Water is thin, meaning lower viscosity. Air is thinner still.

Dynamic viscosity (μ, mu) measures how hard you have to push to make the fluid slide. It is the fundamental physical property of the fluid, independent of density. Units: Pa·s (Pascal-seconds), or the older unit mPa·s (which equals centipoise, cP).

Kinematic viscosity (ν, nu) combines dynamic viscosity with the effect of density. Denser fluids have more inertia and need more force to overcome it, and kinematic viscosity captures this. It is defined as ν = μ/ρ. Units: m²/s, or the convenient unit cSt (centistoke), where 1 cSt = 10⁻⁶ m²/s.

Why kinematic viscosity is used in Reynolds number

The Reynolds number formula is Re = ρVD/μ (using dynamic viscosity) or Re = VD/ν (using kinematic viscosity). Since ν = μ/ρ, these are mathematically identical.

The kinematic form Re = VD/ν is preferred because it is more compact and because kinematic viscosity tables are commonly available for most fluids. When you look up "viscosity of water" in an engineering textbook, the value given is usually kinematic viscosity in m²/s or cSt.

Reference values for common fluids at 20°C

Air has a kinematic viscosity 15 times higher than water, even though it feels far less viscous. This is because air is much less dense. In a Reynolds number calculation, air behaves as if it is relatively more viscous than water, which is why large air velocities are still needed to achieve the same Reynolds number as a water system.

How temperature affects each type

For liquids, both dynamic and kinematic viscosity decrease with temperature. Hot water flows more easily than cold water because higher temperatures give molecules enough energy to overcome intermolecular attraction.

For gases, dynamic viscosity increases with temperature (more molecular collisions means more momentum transfer). But because gas density also decreases with temperature, kinematic viscosity increases even faster. Hot air is therefore "more viscous" in the Reynolds number sense: it produces lower Reynolds numbers at the same velocity and diameter.

Reading the grade off an oil label

Lubricant suppliers rarely print μ or ρ on the drum. They print a grade, and the grade is usually kinematic viscosity already, which saves you the conversion entirely once you know how to read it.

An ISO viscosity grade is the simplest case. The number in ISO VG 46 is the nominal kinematic viscosity in centistokes at 40°C, held within ±10%. So ISO VG 46 means roughly 46 cSt, which is 4.6 × 10⁻⁵ m²/s, and it goes straight into a Reynolds number with no arithmetic at all. ISO VG 32, 46, 68, and 100 cover most hydraulic and circulating oils.

SAE engine oil grades work differently and catch people out. A single grade like SAE 30 is defined at 100°C, not 40°C, so the number is not comparable to an ISO VG figure. A multigrade such as 10W-40 encodes two separate tests: the 10W comes from cold-cranking behaviour at low temperature, and the 40 from kinematic viscosity at 100°C. Neither number is the viscosity at your operating temperature unless that temperature happens to be 100°C.

When the grade does not match the temperature you care about, ask the supplier for the viscosity index or a viscosity-temperature chart for that specific product. Interpolating between two published points beats guessing, and for oils the error from guessing is large: the same oil can change viscosity by an order of magnitude between a cold start and normal running temperature.

A worked conversion, and why it matters

A gear oil data sheet gives dynamic viscosity as 0.22 Pa·s and density as 890 kg/m³ at 40°C. Neither number goes into the Reynolds number directly, so convert first:

Now push that oil through a 50 mm pipe at 1.5 m/s. Re = VD/ν = (1.5 × 0.05) / 2.47 × 10⁻⁴, which comes to about 304. That is firmly laminar, so the friction factor is simply 64/Re and the Moody chart curves never come into it.

Run water through the same pipe at the same speed and Re is about 74,700. Same geometry, same velocity, turbulent flow, and a friction factor that now depends on pipe roughness. The only thing that changed was viscosity. This is why using a room-temperature value, or the wrong viscosity type altogether, can put you on the wrong side of the transition and give a friction factor that is wrong by a factor of two or more.

Where ν = μ/ρ stops working

This relationship assumes a Newtonian fluid, meaning viscosity stays the same no matter how hard you shear it. Water, air, refined oils, and most solvents behave this way across normal pipe velocities, so a single viscosity value describes them completely.

Slurries, drilling muds, polymer solutions, paints, and blood do not. Their apparent viscosity changes with shear rate, so there is no single ν to look up, no single Reynolds number, and no valid Moody chart lookup. Those fluids need a rheological model such as power-law or Bingham plastic, plus a modified Reynolds number built for that model. If your fluid thickens when it sits or thins when you pump it harder, the calculators on this site will give you a number, but it will not describe your system.

Practical tips for engineers

• When using the Reynolds Number Calculator, use kinematic viscosity (ν) in m²/s. For water at 20°C: 1.004 × 10⁻⁶ m²/s is a safe default.
• When your data sheet only lists μ and ρ, use the Kinematic Viscosity Calculator to convert: ν = μ/ρ.
• Always use viscosity at the operating temperature, not room temperature. Getting water 10°C wrong shifts viscosity by about 20%. Getting it 20°C wrong shifts it by about a third.
• For mixtures and non-standard fluids, consult a chemical engineering reference or use measurement data.

Frequently asked questions