Free Poise-Stokes Converter

This poise-stokes converter is a versatile tool for converting between dynamic viscosity (poise) and kinematic viscosity (stokes) and vice versa. With this viscosity converter, you can quickly transform values from poise to stokes or stokes to poise, and also explore equivalent units. The following sections explain the difference between the two viscosity types, how they are related, and the simple conversion process.

Dynamic and Kinematic Viscosity: A Quick Overview

Viscosity describes a fluid's resistance to flow—often referred to as its "thickness." However, this property can be examined from two angles:

• Dynamic viscosity (η) measures the internal resistance when a force is applied to make the fluid move. It answers the question: how much force is required to achieve a certain flow rate? For example, a toothpaste formulation uses dynamic viscosity to ensure the product squeezes out easily but doesn't run excessively.
• Kinematic viscosity (ν) describes how fast a fluid moves under an applied force. It is key in applications like fuel injection, where the speed of fuel droplets leaving a nozzle depends on the fluid's kinematic viscosity.

The two are connected through the fluid's density (ρ).

Poise and Stokes: The Standard Units

Dynamic viscosity is measured in poise (P), after Jean Poiseuille. One poise equals 0.1 pascal-seconds (Pa·s). For convenience, submultiples like centipoise (cP) are common. The following table lists the equivalent values of 1 poise across various unit systems:

Unit	Value per 1 poise
centipoise (cP)	100
millipascal seconds (mPa·s)	100
pascal seconds (Pa·s)	0.1
slugs per foot second (slug/(ft·s))	0.00209
pound-force second per square foot (lbf·s/ft²)	0.00209
pounds per foot second (lb/(ft·s))	0.06720
dyne-second per square centimeter (dyn·s/cm²)	1
gram per centimeter second (g/(cm·s))	1
kilogram per meter second (kg/(m·s))	0.1
reyn	0.0000145

Kinematic viscosity is measured in stokes (St), named after George Gabriel Stokes. One stoke equals 1 square centimeter per second (cm²/s). Again, centistokes (cSt) are widely used. The equivalents for 1 stoke are:

Unit	Value per 1 stoke
centistokes (cSt)	100
square millimeters per second (mm²/s)	100
square centimeters per second (cm²/s)	1
square meters per second (m²/s)	0.00010
square inches per second (in²/s)	0.15500
square feet per second (ft²/s)	0.00108

Note: In everyday viscosity measurements, centipoise (cP) and centistokes (cSt) are the most common units because they produce numbers in a convenient range.

The Conversion Formula

To convert between dynamic and kinematic viscosity, you always need the fluid’s density at the same temperature. The fundamental relationship is:

$$\nu = \frac{\eta}{\rho}$$

where:

• $\nu$ = kinematic viscosity in stokes (St)
• $\eta$ = dynamic viscosity in poise (P)
• $\rho$ = density in grams per cubic centimeter (g/cm³)

Rearranging gives the reverse formula:

$$\eta = \nu \times \rho$$

Thus, converting stokes to poise simply multiplies the kinematic viscosity by the density.

Important considerations:

• Both viscosity values and density must refer to the same temperature, as these properties change with temperature.
• Always use consistent units: dynamic viscosity in poise, density in g/cm³, kinematic viscosity in stokes. If your density is given in kilograms per cubic meter (kg/m³), divide it by 1000 to obtain g/cm³ before using the formula.
• If your input values are in different units (e.g., centipoise, centistokes), convert them to the base units first to avoid errors.

Practical Examples

Example 1: Water at 20°C

Water at 20°C has a density of roughly 0.9982 g/cm³ and a dynamic viscosity of about 0.010016 poise. The equivalent kinematic viscosity is:

$$\nu = \frac{0.010016\ \mathrm{P}}{0.9982\ \mathrm{g/cm^3}} = 0.010034\ \mathrm{St}$$

This value corresponds to 1.0034 centistokes (cSt).

Example 2: Diesel fuel

A diesel sample has a kinematic viscosity of 0.025 stokes. With a typical density of 0.9 g/cm³, its dynamic viscosity becomes:

$$\eta = 0.025\ \mathrm{St} \times 0.9\ \mathrm{g/cm^3} = 0.0225\ \mathrm{P}$$

Equivalently, this is 2.25 centipoise (cP).

These examples illustrate how the conversion works in both directions.

How to Use the Poise-Stokes Converter

The converter simplifies these calculations. Follow these steps:

1. Enter the density of your fluid in g/cm³ (or kg/m³, which will be automatically converted).
2. Input your known viscosity – either dynamic or kinematic.
3. The tool instantly displays the corresponding viscosity in the other type.
4. You can also view the result in alternative units (e.g., cP, mPa·s, cSt, mm²/s) by selecting a different unit from the dropdown menu.

No manual formula application is necessary—the calculator handles all conversions for you.