Viscosity Converter — dynamic and kinematic, kept separate

The viscosity converter above does one thing that most viscosity tools get wrong: it treats dynamic viscosity and kinematic viscosity as the two separate physical quantities they actually are. They have different dimensions, different SI units, and different numerical values for the same fluid. Converting between them requires the fluid density, and any tool that silently assumes a density is producing a number you cannot trust.

Arb Digital maintains this converter as part of a free technical reference library. The factors come from the SI definitions published by the BIPM and the conversion tables in NIST Special Publication 811, and the exact ones, including the international foot, the pound-force and the pound-mass, are carried at full precision rather than rounded.

What This Viscosity Converter Does

Pick a quantity first. In dynamic mode the converter works in pascal-seconds and everything that reduces to them: millipascal-seconds, poise, centipoise, micropoise, dyne-seconds per square centimetre, pound-force-seconds per square foot, the reyn, and the pound-mass per foot-second used in older thermodynamics texts. In kinematic mode it works in square metres per second and its relatives: stokes, centistokes, square millimetres per second, square feet per second and square inches per second.

The headline result gives your requested conversion. The four supporting panels show the same fluid property in the SI unit for that mode, in the two centimetre-gram-second units that dominate industrial practice, and finally in the other quantity, calculated using the density you supply. That fourth panel is the one that saves the most time in practice, because lubricant, coolant and polymer datasheets rarely all quote the same quantity.

How to Use It

1. Choose dynamic or kinematic. If your figure is in Pa·s, poise or centipoise it is dynamic. If it is in m²/s, stokes or centistokes it is kinematic. An ISO VG grade number is kinematic viscosity in cSt at 40 °C.
2. Enter the value. The default is 1.002, the dynamic viscosity of pure water at 20 °C in centipoise.
3. Set the from and to units. The lists reload to show only units valid for the quantity you selected, so a mixed conversion is impossible by construction.
4. Enter the fluid density if you want the cross-conversion panel to be meaningful. Without the correct density, the dynamic-to-kinematic relationship cannot be evaluated at all.
5. Read the four panels for the same property in the units most likely to appear on a supplier datasheet, and use Swap to check the inverse.

The Formula and How It Is Calculated

Dynamic viscosity, symbol μ or η, is the ratio of shear stress to shear rate in a fluid. Shear stress has units of pascals and shear rate has units of reciprocal seconds, so the SI unit is the pascal-second, equivalently kg·m⁻¹·s⁻¹. The centimetre-gram-second unit is the poise, equal to exactly 0.1 Pa·s, and the centipoise is exactly 0.001 Pa·s, which happens to sit almost exactly at the viscosity of water at room temperature. That coincidence is why the centipoise survives in industry long after the rest of the CGS system was retired.

Kinematic viscosity, symbol ν, is dynamic viscosity divided by mass density: ν = μ ÷ ρ. Dividing Pa·s by kg/m³ leaves m²/s, a unit of area per time with no mass in it at all. The CGS unit is the stokes, exactly 10⁻⁴ m²/s, and the centistokes is exactly 10⁻⁶ m²/s, which is also exactly one square millimetre per second. Both the BIPM SI Brochure and NIST Special Publication 811 list the poise and stokes as CGS units accepted for limited use with exact decimal relationships to the SI units, and those exact relationships are what this converter applies.

Dynamic Versus Kinematic: The Error That Ruins Calculations

Conflating the two is the most common mistake in fluid work, and it is easy to make because the words sound interchangeable and the numbers are often the same order of magnitude. They are not the same quantity. Dynamic viscosity answers the question of how much stress it takes to shear a fluid at a given rate. Kinematic viscosity answers how quickly momentum diffuses through the fluid relative to its own inertia.

Which one you need depends on the equation. Reynolds number is conventionally written with kinematic viscosity in the denominator, so feeding it a centipoise figure without dividing by density gives a Reynolds number wrong by roughly a factor of a thousand for a liquid. Pressure-drop and torque calculations, by contrast, usually want dynamic viscosity directly. A useful discipline is to check the dimensions of the target formula before choosing which number to look up, because the units themselves will tell you which quantity the equation expects.

Why cP and cSt Are Not Interchangeable

For water at room temperature, dynamic viscosity is about 1.002 cP and kinematic viscosity is about 1.004 cSt. Those numbers being nearly identical has misled generations of people into treating cP and cSt as the same unit. The equality only holds because water density is close to 1000 kg/m³, which makes the division by density almost a division by one when the units are chosen that way.

Step away from water and the equivalence collapses. A typical mineral gear oil with a density near 880 kg/m³ and a kinematic viscosity of 220 cSt has a dynamic viscosity of about 194 cP, a 12% difference. Mercury is far more dramatic: at 13,534 kg/m³ its dynamic viscosity of roughly 1.53 cP corresponds to a kinematic viscosity of only about 0.113 cSt, a factor of thirteen apart. Whenever a fluid density is far from 1000 kg/m³, treat the two numbers as unrelated until you have done the division. If you need to convert the density itself, the density converter handles kg/m³, g/cm³ and lb/ft³.

Viscosity Without a Temperature Is Not a Specification

Viscosity is strongly temperature dependent, far more so than density or most other fluid properties. Water at 0 °C is roughly 1.79 cP; at 100 °C it falls to about 0.28 cP, a sixfold change across the liquid range. Lubricating oils change even more steeply, which is exactly why viscosity index exists as a measure of how flat that curve is.

This means a viscosity value quoted without a temperature is incomplete. Industry conventions fill the gap: ISO VG grades are defined at 40 °C, SAE engine oil grades reference both 100 °C and low-temperature cranking conditions, and most chemical handbooks default to 20 or 25 °C. When you convert a number with this tool, the temperature travels with it unchanged, so carry the temperature label into whatever you write down next. Converting units never converts conditions.

Saybolt Seconds and Other Non-Linear Scales

Some legacy viscosity scales are not units at all in the SI sense. Saybolt Universal Seconds, Redwood seconds and Engler degrees are efflux times measured by timing a fixed volume of fluid draining through a standard orifice. The relationship between an efflux time and true kinematic viscosity is non-linear, especially at low viscosity where surface tension and kinetic energy corrections dominate, and the standard conversions are published as empirical tables rather than a single multiplier.

This converter deliberately omits them rather than presenting a fabricated linear factor, which is what several competing tools do. Above roughly 50 cSt the approximation SUS ≈ 4.6 × cSt becomes reasonable, but below that the error grows quickly and a proper conversion needs the correction table from the relevant test standard. Presenting a fake exact factor for an empirically defined scale would be worse than not offering it.

Non-Newtonian Fluids: When One Number Is Not Enough

Everything above assumes a Newtonian fluid, meaning shear stress is proportional to shear rate and viscosity is a single constant at a given temperature. Water, air, light oils and most solvents behave this way. Many industrially important fluids do not. Paints, drilling muds, polymer melts, ketchup, blood and toothpaste all have a viscosity that depends on how fast they are being sheared, and often on how long they have been sheared.

For these fluids the correct term is apparent viscosity, and it is only meaningful alongside the shear rate at which it was measured. A shear-thinning paint might read 20,000 cP under a slow spindle and 200 cP at spray-gun shear rates, and both figures are correct. Converting either one between units is perfectly valid, but comparing two apparent viscosities measured at different shear rates is not. Check the measurement conditions before you compare, and treat any single-number viscosity spec for a suspension or polymer with appropriate caution.

Full Viscosity Conversion Tables

Dynamic viscosity factors, expressed as the value of one unit in pascal-seconds:

Kinematic viscosity factors, expressed as the value of one unit in square metres per second:

Common Mistakes to Avoid

• Treating cP and cSt as the same unit — they are equal only when density is 1000 kg/m³, and the error scales directly with how far your fluid sits from that value.
• Quoting viscosity without a temperature — the number can vary sixfold across a fluid's liquid range, so a bare value is not a specification.
• Feeding dynamic viscosity into a Reynolds number formula that expects kinematic viscosity, which throws the result off by roughly the density in kg/m³.
• Using a fixed multiplier for Saybolt seconds — that scale is empirical and non-linear, and single-factor conversions fail badly at low viscosity.
• Comparing apparent viscosities of non-Newtonian fluids measured at different shear rates as though they were the same property.

Related Free Tools From Arb Digital

Viscosity work rarely stands alone. Convert the density term with the density converter, handle head and pressure drop with the pressure converter, size a line with the flow rate converter, and convert pipe or plate geometry with the area converter and length converter. Temperature conditions can be converted in the temperature converter, and the general unit converter covers everything else.

Frequently Asked Questions

This converter is a unit reference only. Viscosity values used for lubrication, process design, or safety decisions should come from a measured datasheet at the stated temperature and shear conditions.