Viscosity Converter

A viscosity converter translates a single fluid property, how much a fluid resists flowing, between two related families of units. The dynamic family (pascal-seconds, millipascal-seconds, poise, centipoise, and two imperial/US variants) describes a fluid's internal friction under a shear stress. The kinematic family (square metres per second, stokes, centistokes, square millimetres per second, and square feet per second) describes the same property divided by the fluid's density. Both families are needed in industry: dynamic viscosity governs force-driven flow problems (bearing lubrication, polymer extrusion), while kinematic viscosity governs gravity- and pressure-driven flow problems (pipe flow, capillary viscometry, petroleum specifications). This converter keeps both panels in sync and ties them together with the density bridge ν = μ / ρ, so you can move freely between the two without losing track of what is a property of the fluid and what is a property of the unit system.

How to Use the Viscosity Converter

1. Type a dynamic viscosity into any of the six fields in the Dynamic panel. The other five update instantly through a pascal-second pivot. The same applies to the five fields in the Kinematic panel, which pivot through square metres per second.
2. The two panels are independent, they do not auto-sync, because no automatic relationship exists between dynamic and kinematic viscosity without also knowing the density.
3. Enter a density in the Density bridge panel. The bridge then shows the kinematic viscosity implied by the current dynamic value (μ / ρ), and the dynamic viscosity implied by the current kinematic value (ν × ρ). These are not edit fields, they tell you what the other panel would say if the density you entered were correct for the fluid.
4. Use the Reference fluids presets for a quick load of typical order-of-magnitude values for water, air, light machine oil, honey, and glycerine near room temperature.
5. Treat every preset and every input as approximate. Viscosity shifts by large factors across modest temperature changes, so any value quoted without a temperature is an order-of-magnitude estimate, not a specification.
6. Round only at the end of your calculation; the converter carries the full internal precision through every step.

The Formulas

Dynamic viscosity, pivot Pa·s. Every dynamic viscosity unit is an exact multiple of the pascal-second:

• 1 P = 0.1 Pa·s
• 1 cP = 0.001 Pa·s = 1 mPa·s
• 1 lbf·s/ft² = 47.88025898033584 Pa·s
• 1 lb/(ft·s) = 1.4881639435695538 Pa·s
• 1 Pa·s = 1 Pa·s (the SI unit)

These factors are exact, or exact to the digits shown, under NIST SP 811 and the SI Brochure. The CGS factors follow from 1 P = 1 g/(cm·s) = 0.1 kg/(m·s) = 0.1 Pa·s. The imperial factors follow from the pound-force (4.4482216152605 N exactly) and the foot (0.3048 m exactly).

Kinematic viscosity, pivot m²/s. Every kinematic viscosity unit is an exact multiple of the square metre per second:

• 1 St = 1e-4 m²/s
• 1 cSt = 1e-6 m²/s = 1 mm²/s
• 1 ft²/s = 0.09290304 m²/s (exact, since 1 ft = 0.3048 m exactly)

The stokes is named after George Gabriel Stokes, whose work on fluid mechanics produced the Navier-Stokes equations. The factor 1 St = 1 cm²/s = 1e-4 m²/s is exact under the CGS-to-SI conversion.

The density bridge, ν = μ / ρ. Kinematic viscosity is defined as dynamic viscosity divided by density. In SI units, μ has dimensions of Pa·s (kg/(m·s)) and ρ has dimensions of kg/m³, so ν has dimensions of m²/s. To move from the dynamic panel to the kinematic panel, supply ρ; to move the other way, supply ρ again. No converter can do this for you without a density input, that is why this tool exposes the bridge as a separate, editable panel rather than baking an assumed density into the conversion.

Worked Examples

Example 1, Round-trip inside the dynamic panel. Convert 1 Pa·s into centipoise and back. 1 Pa·s ÷ 0.001 Pa·s per cP = 1000 cP. Reverse: 1000 cP × 0.001 = 1 Pa·s. Round trip is exact.

Example 2, Round-trip inside the kinematic panel. Convert 1 m²/s into centistokes and back. 1 m²/s ÷ 1e-6 m²/s per cSt = 1e6 cSt. Reverse: 1e6 cSt × 1e-6 = 1 m²/s. Round trip is exact.

Example 3, Imperial dynamic to SI. Convert 1 lbf·s/ft² to pascal-seconds. 1 lbf·s/ft² × 47.88025898033584 = 47.88025898033584 Pa·s (exact to the digits shown).

Example 4, Imperial kinematic to SI. Convert 1 ft²/s to m²/s and cSt. 1 ft²/s × 0.09290304 = 0.09290304 m²/s. In centistokes: 0.09290304 m²/s × 1e6 = 92903.04 cSt.

Example 5, The bridge for water. Liquid water near 20 °C has dynamic viscosity μ ≈ 0.001 Pa·s = 1 mPa·s = 1 cP and density ρ ≈ 998 kg/m³. The implied kinematic viscosity is:

ν = μ / ρ = 0.001 / 998 ≈ 1.002e-6 m²/s ≈ 1.002 cSt ≈ 1.002 mm²/s.

Example 6, The bridge for air. Air at 20 °C has dynamic viscosity around μ ≈ 1.8e-5 Pa·s and density ρ ≈ 1.20 kg/m³. The implied kinematic viscosity is:

ν = 1.8e-5 / 1.20 ≈ 1.5e-5 m²/s ≈ 15 cSt.

Air is roughly fifteen times more kinematically viscous than water at the same temperature, even though its dynamic viscosity is about fifty-five times smaller.

Where Viscosity Conversion Shows Up

Petroleum and lubricant specifications. Engine oils, hydraulic fluids, gear oils, and turbine oils are specified by kinematic viscosity at 40 °C and 100 °C, in mm²/s (identical to cSt). ISO 3104 defines the standard capillary method; ASTM D2270 then converts those two measurements into the dimensionless Viscosity Index (VI), a measure of how strongly the oil thins as it warms up. A high VI means the oil stays closer to a single viscosity across temperature, the property that defines a "multigrade" oil (5W-30, 10W-40, etc.).

Polymer processing, food, cosmetics, paint. Polymer melts, syrups, gels, toothpastes, shampoos, and paints are routinely characterised in cP at a specified temperature and shear rate. Quality-control release tests compare a batch against a viscosity range, not a single value. These are not specification data for any particular product, just typical order-of-magnitude ranges.

Biomedical and laboratory. Blood is a shear-thinning fluid (around 3 to 5 mPa·s at high shear, 10 to 20 mPa·s at low shear, plasma around 1.2 mPa·s). The numerical conversion between cP and mPa·s is a no-op (1 cP = 1 mPa·s, exactly).

Common Mistakes

Treating poise and stokes as interchangeable. Poise (P) is dynamic; stokes (St) is kinematic. The numerical values for water at room temperature happen to be 1 cP and 1 cSt, a coincidence of density (1 g/cm³ = 1000 kg/m³) and the factor-of-100 difference between cP→P and cSt→St. For fluids with densities other than 1 g/cm³, the numbers diverge.

Quoting viscosity without a temperature. Liquid viscosities drop by roughly an order of magnitude between near-freezing and near-boiling. Gas viscosities rise with temperature, but more gently (typically less than a factor of two). A "viscosity of 1 mPa·s" without a temperature is meaningless, water at 0 °C is around 1.79 mPa·s, water at 20 °C is around 1.00 mPa·s, water at 90 °C is around 0.32 mPa·s.

Confusing the bridge direction. To get kinematic from dynamic: divide by density. To get dynamic from kinematic: multiply by density. Both directions require the density.

Confusing viscosity with viscosity index. Viscosity is a measured quantity with units. Viscosity index is a derived, dimensionless number from ASTM D2270 that describes how viscosity changes with temperature. The two are related but not interchangeable. A high-viscosity oil may have a low VI (thins fast with temperature) and a low-viscosity oil may have a high VI (holds its viscosity as it warms).

Assuming a brand-specific viscosity from memory. Motor oils, gear oils, hydraulic fluids, and cosmetic products vary enormously by formulation and temperature. "10W-30 motor oil" is a viscosity-grade specification, not a viscosity value, different brands at the same grade have measurably different viscosity curves. Read the data sheet.

Newtonian and Non-Newtonian Fluids

A Newtonian fluid has a viscosity that does not depend on the shear rate, push it harder and it resists proportionally harder, with the same proportionality constant. Water, air, most simple oils, and most gases are Newtonian to a good approximation.

A non-Newtonian fluid has a viscosity that depends on the shear rate (and sometimes on the shear history). The common classes are:

• Shear-thinning (pseudoplastic), viscosity falls as shear rate rises. Examples: ketchup, paint, blood, polymer melts.
• Shear-thickening (dilatant), viscosity rises as shear rate rises. Examples: concentrated cornstarch suspensions (the "oobleck" you can run across), wet sand under sudden impact.
• Thixotropic, viscosity falls over time at constant shear, then recovers at rest. Examples: yogurt, drilling mud. Thixotropy is time-dependent shear-thinning.
• Rheopectic, viscosity rises over time at constant shear (rare). Examples: some gypsum pastes.

The converter handles viscosity as a single number, so it is directly applicable to Newtonian fluids. For non-Newtonian fluids it gives you a single-point viscosity at whatever shear rate your measurement was made. To characterise one properly, you need a flow curve: viscosity versus shear rate, fitted to a model (power-law, Carreau, Cross, Bingham, Herschel-Bulkley).

Temperature Dependence

Viscosity is among the most strongly temperature-dependent physical properties. For most liquids the dynamic viscosity drops by roughly an order of magnitude between near-freezing and near-boiling, and the drop is well-described by an Arrhenius-type relation:

μ(T) ≈ μ₀ · exp(E / (R · T))

where T is absolute temperature, μ₀ is a reference viscosity, E is an activation energy, and R is the gas constant. E typically falls in the range of 10 to 30 kJ/mol for simple liquids and higher for very viscous fluids.

For gases the behaviour is reversed, viscosity rises with temperature, but only mildly. The mechanism is different: in liquids, increased temperature reduces the cohesive forces between molecules (so flow becomes easier); in gases, increased temperature increases the rate of molecular momentum exchange (so resistance to flow grows). Air's viscosity roughly doubles between 0 °C and 600 °C, whereas a typical oil's viscosity drops by orders of magnitude across that range.

Because of this strong temperature dependence, the converter's reference-fluid presets are quoted at "approximately room temperature" with no tighter specification. Do not use the presets to estimate the viscosity of any specific product at any specific temperature; read the data sheet.

Measurement Methods

Capillary viscometry. A measured volume of fluid flows through a narrow tube under gravity, and the time taken is related to the kinematic viscosity by the Hagen-Poiseuille equation. Capillary viscometers are the standard method for petroleum products (ISO 3104), and the kinematic viscosity is read directly in mm²/s = cSt. Glass capillary viscometers (Cannon-Fenske, Ubbelohde) are the laboratory workhorse.

Rotational viscometry. A spindle rotates in the fluid at a controlled speed, and the torque required to maintain that speed is measured. The dynamic viscosity is read directly in mPa·s or cP (the two are numerically identical). Common geometries include concentric cylinders (Couette), cone-and-plate (ideal for non-Newtonian characterisation), and parallel plates.

Falling-ball viscometry. A ball of known density and diameter falls through the fluid under gravity, and the terminal velocity is related to the dynamic viscosity by Stokes' law. Falling-ball viscometers are simple and reliable, suitable for opaque fluids and high-viscosity samples.

Frequently Asked Questions

Why are there two different kinds of viscosity at all?

Dynamic viscosity (μ) is the fundamental quantity: the constant of proportionality between a shear stress and the shear rate it produces. Kinematic viscosity (ν = μ / ρ) is a derived quantity: the natural variable in gravity- and pressure-driven flow problems (pipe flow, capillary viscometry) where the fluid's inertia and weight are both relevant. Converting between them always requires knowing the density.

Can I convert a cP value to a cSt value directly?

Only if the density is exactly 1 g/cm³. For any other fluid, oil, syrup, glycerol, honey, you must divide cP by density (in g/cm³) to get cSt. The numerical coincidence at water density is the source of the most common viscosity-conversion error in elementary work.

What is the relationship between viscosity and viscosity index (VI)?

Viscosity index is a derived, dimensionless number from ASTM D2270 that captures how strongly an oil's viscosity changes with temperature. Two oils can have the same viscosity at 40 °C and very different viscosities at 100 °C; the one whose viscosity changes less has the higher VI. Multigrade oils (5W-30, 10W-40) are formulated with viscosity-index improvers, polymeric additives that unfold at higher temperatures to thicken the oil and compensate for thermal thinning.

How does temperature affect viscosity?

Strongly, and in opposite directions for liquids and gases. Liquid viscosities typically drop by roughly an order of magnitude between near-freezing and near-boiling, following an Arrhenius-type relation. Gas viscosities rise with temperature but only mildly, typically less than a factor of two over the same temperature range. Liquid flow requires overcoming intermolecular cohesion (which weakens with temperature); gas flow requires momentum transport between molecules (which intensifies with temperature).

What is the difference between shear-thinning and thixotropy?

Shear-thinning is an instantaneous property: at this shear rate, the viscosity is this number. Thixotropy is a time-dependent property: at this shear rate, sustained for this long, the viscosity is this number. Shear-thinning ketchup and thixotropic yogurt both feel "less thick" when you work them, but the ketchup reaches its low-viscosity state instantly while the yogurt needs seconds or minutes.

Why do petroleum and lubricant standards use kinematic viscosity (mm²/s) rather than dynamic viscosity (mPa·s)?

Because the standard test method (ISO 3104) measures the time for a fixed volume to flow through a calibrated capillary under gravity, a direct measurement of kinematic viscosity. Reporting the result in mm²/s = cSt avoids any dependence on the fluid's density in the calculation; the density enters later, only when the user needs to convert the kinematic specification into a dynamic one for force-based calculations.

can the Viscosity Converter (Dynamic & Kinematic) be used for professional or commercial purposes?

yes, the Viscosity Converter (Dynamic & Kinematic) provides mathematically correct results that are suitable for professional, commercial, and educational use. For the Viscosity Converter (Dynamic & Kinematic), For the Viscosity Converter (Dynamic & Kinematic), For high-stakes applications (medical, legal, financial), verify results with a domain expert. For the Viscosity Converter (Dynamic & Kinematic), the Viscosity Converter (Dynamic & Kinematic) formulas used are well-established and validated against reference standards.

For the Viscosity Converter (Dynamic & Kinematic), How often are the underlying formulas updated?

For the Viscosity Converter (Dynamic & Kinematic), the Viscosity Converter (Dynamic & Kinematic) formulas are based on established scientific, mathematical, or industry-standard references and rarely require updates. when standards change, the Viscosity Converter (Dynamic & Kinematic) is updated to reflect the current authoritative source. For the Viscosity Converter (Dynamic & Kinematic), For the Viscosity Converter (Dynamic & Kinematic), Each calculator's references section lists the specific sources used.

References

• NIST Special Publication 811, Guide for the Use of the International System of Units (SI). The authoritative US reference for SI usage, unit conversion, and the exact definitions of derived units including the pascal-second (Pa·s) and the factors relating poise, stokes, and their SI equivalents.
• BIPM SI Brochure (9th edition), The International System of Units (SI). Published by the Bureau International des Poids et Mesures, this is the canonical definition of the SI units, including the conventions for dynamic and kinematic viscosity.
• ISO 80000-4, Quantities and units, Part 4: Mechanics. The international standard for the quantities, symbols, and units of mechanics, including dynamic viscosity (symbol η or μ, unit Pa·s) and kinematic viscosity (symbol ν, unit m²/s), and the relationship ν = μ / ρ.
• ISO 3104, Petroleum products, Transparent and opaque liquids, Determination of kinematic viscosity and calculation of dynamic viscosity. The standard capillary-viscometer method that defines how kinematic viscosity is measured and reported for petroleum products.
• ASTM D2270, Standard Practice for Calculating Viscosity Index from Kinematic Viscosity at 40 °C and 100 °C. The standard method by which the petroleum industry converts two kinematic-viscosity measurements into the dimensionless viscosity index used to grade multigrade oils.
• SI conventions for the poise and the stokes, The CGS-system units named after Jean Léonard Marie Poiseuille and George Gabriel Stokes. The poise is 1 g/(cm·s) = 0.1 Pa·s, and the stokes is 1 cm²/s = 1e-4 m²/s. Their centi- prefixes (cP, cSt) are numerically equal to the SI milli- prefixes (mPa·s, mm²/s).