Viscosity Converter Calculator

Viscosity measures a fluid’s resistance to deformation and flow. Water pours easily because its dynamic viscosity is low; honey, motor oil, paint, and glycerin flow more slowly because their viscosity is higher. This converter changes a known nonnegative dynamic viscosity among the units in the calculator: pascal-second, poise, centipoise, and millipascal-second. It does not calculate flow rate, pressure drop, or temperature correction. It only converts the unit label while preserving the same physical viscosity.

The SI unit for dynamic viscosity is the pascal-second, written Pa·s. One Pa·s is one pascal of shear stress per reciprocal second of velocity gradient. The poise, P, is a centimeter-gram-second unit still found in older fluid references. Centipoise, cP, is one hundredth of a poise and is widely used because water is close to 1 cP near room temperature. Millipascal-second, mPa·s, is the SI-prefixed equivalent of cP; the calculator gives both the same factor.

Defining relationship

For a Newtonian fluid under simple shear, dynamic viscosity relates shear stress to velocity gradient:

$\tau = \mu \frac{du}{dy}$

Here, tau is shear stress, mu is dynamic viscosity, and du over dy is the velocity gradient. The converter assumes you already have mu in one of the supported units. It converts through Pa·s:

$\text{viscosity in target unit} = \frac{\text{input viscosity} \times \text{source factor}}{\text{target factor}}$

Reference table

The exact factors in the calculation are:

From the same table, 1 Pa·s is 10 P, 1000 cP, and 1000 mPa·s. One P is 100 cP. One cP is exactly 1 mPa·s in this converter.

Worked example: pascal-second to centipoise

Suppose the input is 0.75 Pa·s and the target is cP. The source factor for Pa·s is 1, so the base value remains 0.75 Pa·s. The target factor for cP is 0.001 Pa·s per cP:

$\frac{0.75 \times 1}{0.001} = 750$

The calculator displays centipoise to four decimals, so the result is 750.0000 cP. The all-units list reports 0.750000 Pa·s, 7.5000 P, 750.0000 cP, and 750.0000 mPa·s. That last equality is intentional: cP and mPa·s share the same factor in the calculation.

Where each unit is used

Pascal-second is the coherent SI unit and the best choice for equations involving pressure, shear stress, and SI geometry. If you are modeling pipe flow, bearing films, extrusion, mixing, or drag in an SI calculation, Pa·s keeps the algebra clean. For flow-volume conversions without viscosity modeling, use the flow-rate converter.

Poise appears in older CGS tables and in historical fluid mechanics. It is less convenient for modern SI calculations, but many reference materials still list P or cP because the numbers are familiar.

Centipoise is popular in industry because common liquids fall into readable ranges. Water is about 1 cP near ordinary room temperature, light oils may be tens or hundreds of cP, and syrups or coatings may be much higher. Data sheets for adhesives, paints, fuels, and food products often use cP along with a temperature and test method.

Millipascal-second is numerically identical to centipoise but fits SI prefix style. A laboratory may report a fluid as 500 mPa·s instead of 500 cP. The number is the same in this calculator, but the notation may better match standards, instrument software, or customer specifications.

Temperature, density, and common mistakes

Temperature is not optional context. Most liquids become less viscous as they warm, and some change by large factors over a small temperature range. The calculator’s note reminds readers that values are often measured at 20°C unless otherwise stated, but it does not enforce or correct that condition. Use the temperature converter only to align temperature units; it will not transform viscosity data from one temperature to another.

Do not confuse dynamic viscosity with kinematic viscosity. Kinematic viscosity divides dynamic viscosity by density and uses units such as stokes or centistokes. To relate the two, you need density as well as viscosity, so the density converter may be part of the workflow. Entering centistokes as centipoise is only valid when density makes the numerical relationship happen to match, and that is not generally true.

Another pitfall is comparing measurements made with different instruments or shear rates. Many real fluids are non-Newtonian: paint, ketchup, polymer solutions, and slurries can appear thinner or thicker depending on how they are sheared. A unit conversion cannot reconcile those test-condition differences. Match temperature, shear rate, spindle, method, and sample history before treating two values as equivalent.

Sources

• NIST, Guide for the Use of the International System of Units — SI unit and conversion guidance.
• BIPM, The International System of Units — SI unit definitions and derived-unit framework.
• OpenStax, Viscosity and Laminar Flow — viscosity definition and flow context.