Enter a kinematic viscosity (ν) for a single liquid/component to calculate its Viscosity Blending Index/Number (VBI/VBN), or enter a VBI/VBN to convert back to viscosity. For blending multiple liquids, convert each component viscosity to VBI/VBN, take the volume‑fraction‑weighted average of those indices, then convert the averaged VBI/VBN back to a blended viscosity (all at the same temperature, commonly 40 °C for lubricants).

Refutas Equation Calculator

Enter either a kinematic viscosity or a VBI/VBN value to convert between them.

Viscosity Blending Index (Refutas) Formula

\mathrm{VBI}=\mathrm{VBN}=14.534\,\ln\!\big(\ln(\nu+0.8)\big)+10.975

Inverse (to convert a VBI/VBN back to kinematic viscosity in cSt):

\nu=\exp\!\left(\exp\!\left(\frac{\mathrm{VBN}-10.975}{14.534}\right)\right)-0.8

Variables:

  • VBI/VBN is the Viscosity Blending Index/Number (dimensionless).
  • ν is the kinematic viscosity of a single liquid/component in cSt (mm²/s), measured at the same temperature as the blend calculation (commonly 40 °C for lubricant work).

How to Calculate Viscosity Blending Index?

The following steps outline how to use the Refutas method for blending.

  1. Measure (or obtain) the kinematic viscosity of each component liquid in cSt at the same temperature.
  2. Convert each component viscosity to a VBI/VBN using: VBN = 14.534 · ln(ln(ν + 0.8)) + 10.975.
  3. Compute the blended index as a weighted average using volume fractions: VBNblend = Σ (xi · VBNi), where Σxi = 1.
  4. Convert VBNblend back to blended kinematic viscosity using: ν = exp(exp((VBN − 10.975)/14.534)) − 0.8.
  5. Use the calculator above to convert between ν and VBI/VBN (and to check intermediate values).

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Kinematic viscosity, ν = 2.234 cSt

Using the Refutas equation, the corresponding VBI/VBN is approximately 12.492 (dimensionless).

FAQs

What is viscosity and why is it important?

Viscosity is a measure of a fluid's resistance to flow. It describes how thick or thin a fluid is. Understanding viscosity is crucial in many industries, such as lubricants, pharmaceuticals, and food production, because it affects how substances behave and interact in different environments and applications.

How do temperature and pressure affect viscosity?

For liquids, viscosity generally decreases as temperature increases (they flow more easily), while for gases viscosity generally increases with temperature. Increasing pressure tends to increase the viscosity of liquids; for gases near atmospheric pressure the effect is often small, but it can become more significant at high pressures.

What is the difference between dynamic and kinematic viscosity?

Dynamic viscosity (absolute viscosity) measures a fluid's resistance to shear under an applied force and is typically reported in Pa·s (or cP). Kinematic viscosity accounts for density and equals dynamic viscosity divided by density (ν = μ/ρ), typically reported in m²/s or cSt (mm²/s).

Can the Viscosity Blending Index be used for all types of liquids?

The Refutas VBI/VBN method is most commonly used for petroleum and similar miscible Newtonian liquids (such as many lubricating oils). It may be less accurate for non‑Newtonian fluids, emulsions, or liquids that are not fully miscible or that react chemically when mixed.