Viscosity Units Converter
Convert between dynamic viscosity units (Pa·s, mPa·s, Poise, cP) and kinematic viscosity units (m²/s, mm²/s, Stokes, cSt). Enter a value, pick a unit, and add the density to switch between the two families.
Convert Viscosity Units
Viscosity Converter Formula
Where:
- \(\mu\) — dynamic viscosity (Pa·s)
- \(\nu\) — kinematic viscosity (m²/s)
- \(\rho\) — density of the fluid (kg/m³)
The two formulas link dynamic and kinematic viscosity through density. Within each family, units are converted with fixed factors: \(1\ \text{Pa·s} = 10\ \text{P} = 1000\ \text{cP}\) and \(1\ \text{m}^2/\text{s} = 10^4\ \text{St} = 10^6\ \text{cSt}\).
Viscosity Converter – Calculation Example
Example: an oil with dynamic viscosity 100 cP and density 0.85 g/cm³ (850 kg/m³).
\[ \mu = 100\ \text{cP} = 100 \times 0.001 = 0.1\ \text{Pa·s} = 1\ \text{P} \]
\[ \nu = \frac{\mu}{\rho} = \frac{0.1}{850} = 1.17647 \times 10^{-4}\ \text{m}^2/\text{s} \approx 117.65\ \text{cSt} \]
Result: 100 cP equals 0.1 Pa·s, 100 mPa·s, 1 Poise; at 850 kg/m³ it also equals 1.17647 × 10⁻⁴ m²/s, about 117.65 mm²/s (cSt), and 1.17647 St.
How to Use the Viscosity Converter
- Enter your value in the Viscosity value field.
- Choose the unit of that value from the Unit dropdown — dynamic units (Pa·s, mPa·s, Poise, cP) or kinematic units (m²/s, mm²/s, St, cSt).
- Enter the fluid density in the Density (ρ) field and select its unit (kg/m³, g/cm³, or lb/ft³). Density is required because converting between dynamic and kinematic viscosity depends on it.
- Read the results: the calculator shows the equivalent value in every other common unit, split into a dynamic viscosity (μ) block and a kinematic viscosity (ν) block.
Dynamic vs. Kinematic Viscosity
Viscosity describes a fluid's resistance to flow, but it is expressed in two distinct ways. Dynamic viscosity (\(\mu\), also called absolute viscosity) measures the internal friction of the fluid — the shear stress needed to produce a given velocity gradient. Its SI unit is the pascal-second (Pa·s); the older CGS unit is the poise (P), with 1 Pa·s = 10 P. The centipoise (cP) is the most common practical unit, and conveniently 1 cP = 1 mPa·s exactly.
Kinematic viscosity (\(\nu\)) is the ratio of dynamic viscosity to density. It describes how the fluid flows under gravity alone, which is why it appears in Reynolds number calculations, lubrication charts, and fuel specifications. Its SI unit is m²/s; the CGS unit is the stokes (St), and 1 cSt = 1 mm²/s exactly.
The two quantities are linked by density: \(\nu = \mu / \rho\). This is why the calculator asks for density — without it, a value in cP cannot be converted to cSt. For water at 20 °C, \(\mu \approx 1\ \text{cP}\) and \(\nu \approx 1\ \text{cSt}\), because the density of water is close to 1 g/cm³. For oils, which are less dense and far more viscous, the two numbers differ significantly.
When interpreting the result, always check which family a specification refers to. Lubricant datasheets typically quote kinematic viscosity in cSt at 40 °C and 100 °C, while polymer and food-industry data often use dynamic viscosity in mPa·s. Mixing them up leads to errors of an order of magnitude or more.
Conversion Factors and Typical Values
| Unit | Equals |
|---|---|
| 1 Pa·s | 1000 mPa·s = 10 P = 1000 cP |
| 1 mPa·s | 1 cP = 0.001 Pa·s |
| 1 Poise (P) | 0.1 Pa·s = 100 cP |
| 1 m²/s | 10⁶ mm²/s = 10⁴ St = 10⁶ cSt |
| 1 St | 100 cSt = 10⁻⁴ m²/s |
| 1 cSt | 1 mm²/s = 10⁻⁶ m²/s |
For orientation: water at 20 °C is about 1 cP / 1 cSt, honey is roughly 10 000 cP, and a typical SAE 30 motor oil has a kinematic viscosity near 300 cSt at 40 °C.
Assumptions and Limitations
- The conversion between dynamic and kinematic viscosity assumes a single, constant density. Viscosity itself changes strongly with temperature, so use the density and viscosity measured at the same temperature.
- The calculator treats the fluid as a Newtonian fluid, whose viscosity does not depend on shear rate. Non-Newtonian fluids (paints, ketchup, blood, polymer melts) have no single viscosity value, so a converted number is only meaningful at a specific shear condition.
- Density must be greater than zero; the calculator rejects zero or negative values because the division \(\nu = \mu/\rho\) would be undefined.
- Compressible fluids (gases) have low but nonzero viscosities, and their density varies with pressure — enter the density at the actual operating conditions for a correct kinematic value.
If you also need to convert densities between kg/m³, g/cm³, and lb/ft³ for other work, try the Density Converter. Related fluid and thermodynamic tools include the Pressure Converter and the Thermal Conductivity Converter.
Frequently Asked Questions
How do I convert cP to cSt without a calculator?
Use the shortcut: if the density is expressed in g/cm³, then cSt = cP / ρ. For example, a fluid of 250 cP with a density of 1.25 g/cm³ gives 250 / 1.25 = 200 cSt. This works because 1 cP = 1 mPa·s and 1 cSt = 1 mm²/s, so the SI prefixes cancel and only the density ratio remains. For quick estimates, oils with density near 0.85 g/cm³ have a cSt value about 18% higher than their cP value.
What is a normal or good viscosity value?
It depends entirely on the fluid and its temperature. For orientation: water at 20 °C is about 1 cP, milk 2–3 cP, olive oil around 80 cP, and honey roughly 10 000 cP. Motor oils are usually specified by kinematic viscosity: an SAE 30 oil is near 100 cSt at 40 °C and about 10 cSt at 100 °C. There is no universal "good" value — always compare against the specification for your specific fluid and temperature.
Why does my converted value change with temperature?
Both viscosity and density are temperature-dependent, and viscosity changes dramatically — many oils become roughly twice as fluid for every 10–15 °C of warming. Always use a viscosity value and a density value measured at the same temperature, or your conversion between cP and cSt will be wrong. Lubricant datasheets therefore quote viscosity at standardized temperatures, most commonly 40 °C and 100 °C, so pick the pair that matches your operating condition.
Can I convert Saybolt seconds (SSU) or other practical units here?
Not directly — this converter handles only Pa·s, mPa·s, Poise, cP, m²/s, mm²/s, Stokes, and cSt. However, there are approximate bridges: SSU ≈ cSt × 4.635 for values above about 70 SSU, and Redwood and Engler seconds have similar empirical correlations. Convert your practical unit to cSt first, then use this tool with the fluid density to obtain dynamic units like cP. Note these bridging formulas are approximations, not exact conversions.
How do I convert from English units like lb/(ft·s) or reyn?
Use the fixed factors: 1 lb/(ft·s) = 1.48816 Pa·s, and 1 reyn = 6894.76 Pa·s. For kinematic units, 1 ft²/s = 0.092903 m²/s. Convert your English unit to Pa·s or m²/s first, then enter it here to get all the metric equivalents at once. Density in lb/ft³ can be entered directly in the density field, since 1 lb/ft³ = 16.0185 kg/m³ is handled automatically.
Can I use this converter for gases?
Yes, but enter the gas density at the actual pressure and temperature, because gas density varies strongly with both. Air at 20 °C and 1 atm has a dynamic viscosity of about 0.018 cP and a density near 1.2 kg/m³, giving roughly 15 cSt — a much larger kinematic value than water despite the lower dynamic viscosity. Using the standard-condition density for a compressed gas would give a significantly wrong kinematic viscosity.
What is the most common mistake when converting viscosity units?
Confusing dynamic and kinematic units, especially cP and cSt. They numerically coincide only for fluids with a density of 1 g/cm³, like water. For a typical oil at 0.85 g/cm³, treating 100 cP as 100 cSt introduces an error of about 18%. The second most common mistake is combining a viscosity measured at one temperature with a density from another. If your datasheet quotes cSt at 40 °C, use the density at 40 °C as well.