Fluid Viscosity Calculator

Dynamic (Absolute) Viscosity η (eta)

η = τ / (du/dy), where τ is shear stress in Pa and du/dy is the velocity gradient in 1/s.

SI unit: Pa·s (Pascal-second) = 1000 mPa·s = 1000 cP. Water at 20°C is about 1.002 cP, which is the convenient reference the whole centipoise scale was built around.

Kinematic Viscosity ν (nu)

ν = η / ρ, where ρ is the fluid density in kg/m³.

SI unit m²/s, common unit cSt (centistokes) = mm²/s. Water at 20°C is about 1.004 cSt, near enough to 1 that it makes another handy anchor.

Which one do you actually need?

This trips people up constantly, so it is worth being blunt about it. Dynamic viscosity is the honest measure of a fluid’s internal friction: how hard it resists being sheared. Kinematic viscosity divides that by density, and it is what appears in flow equations because inertia scales with density too.

The practical consequence is counterintuitive. Air has a dynamic viscosity 55 times lower than water, yet its kinematic viscosity is 15 times higher, because air is roughly 830 times less dense. So air is stickier than water in the sense that matters for Reynolds number. Anything to do with pipe flow, boundary layers or Reynolds number wants ν. Anything to do with force on a surface, pumping torque or lubricant film strength wants η.

Viscosity and Temperature

Liquids get thinner as they warm, and dramatically so: water loses roughly 2 to 2.5% of its viscosity per degree Celsius near room temperature, and drops by a factor of six between 0°C and 100°C. Gases go the other way and get thicker when heated, because in a gas the viscosity comes from molecules carrying momentum across the flow, and hotter molecules do that faster.

The Andrade equation fits liquids well: η = A × exp(B/T) with T in Kelvin. For water over 0 to 100°C the standard fit is η ≈ 2.414×10⁻⁵ × 10^(247.8/(T−140)) Pa·s. It is accurate to under 1% across most of that range and drifts to about 2% low right at the freezing point, which is where the “water viscosity at temperature” mode above is at its weakest.

Reynolds Number

Re = ρVL/η = VL/ν, where V is velocity in m/s and L is a characteristic length, usually pipe diameter.

Re < 2300 is laminar, 2300 to 4000 is the transition, above 4000 is turbulent. Those thresholds are for flow in a round pipe and nothing else. A flat plate transitions nearer Re = 500,000 and a sphere behaves differently again, so quoting 2300 for anything other than a pipe is a common and expensive mistake.

Common Unit Conversions

1 Pa·s = 1000 mPa·s = 1000 cP = 10 P (Poise). 1 m²/s = 10⁶ cSt = 10⁶ mm²/s.

Saybolt Universal Seconds is an old empirical scale, still printed on oil datasheets, measuring how long a fixed volume takes to drain through a standard orifice. Converting it takes two correlations: ν(cSt) ≈ 0.226 × SSU − 195/SSU for 32 to 100 SSU, and ν ≈ 0.220 × SSU − 135/SSU above that. The scale starts at 32 because that is roughly water’s own drain time; below 32 the formula returns a negative number and means nothing.

Typical Viscosities (at about 20°C)

Pitch is worth a second look. At 2×10¹¹ cP it is roughly 200 billion times more viscous than water, which is why the famous University of Queensland experiment has produced only nine drops since 1927. It is still a liquid, just an extremely patient one.

One caveat on that table: it assumes Newtonian fluids, where viscosity does not depend on how hard you shear them. Blood, ketchup, paint and most polymer melts are not Newtonian, so a single number for them is a convenient fiction. Blood in particular thins as it flows faster, which is exactly what you want in a capillary.