Convert kinematic viscosity in cSt, St, or m²/s to VBI/VBN, or calculate viscosity from a VBI/VBN value using the Refutas equation.

Refutas Equation Calculator

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

Refutas Equation Formula

The Refutas equation converts kinematic viscosity into a viscosity blending number, also called VBN or VBI. The inverse equation converts VBN/VBI back into kinematic viscosity.

VBN = 14.534 \ln(\ln(\nu + 0.8)) + 10.975
\nu = e^{e^{(VBN - 10.975)/14.534}} - 0.8

Unit conversions used before or after the Refutas equation:

\nu_{cSt} = \nu_{St} \times 100
\nu_{cSt} = \nu_{m^2/s} \times 1,000,000
  • VBN or VBI = viscosity blending number or viscosity blending index, dimensionless
  • ν = kinematic viscosity in centistokes, cSt, for the Refutas equation
  • ln = natural logarithm
  • e = Euler's number
  • cSt = centistokes, numerically equal to mm²/s
  • St = stokes
  • m²/s = square meters per second

If you enter kinematic viscosity, the calculator first converts it to cSt, then calculates VBN/VBI. If you enter VBN/VBI, it uses the inverse Refutas equation to calculate kinematic viscosity. The calculated viscosity can then be shown in cSt, St, or m²/s.

The Refutas equation requires kinematic viscosity greater than 0.2 cSt because the double logarithm must be defined.

Common Kinematic Viscosity Unit Conversions

Unit Equivalent in cSt Notes
1 cSt 1 cSt Same as 1 mm²/s
1 St 100 cSt Used less often than cSt
1 m²/s 1,000,000 cSt SI base-area unit form

Typical VBN Values for Selected Viscosities

Kinematic Viscosity Approximate VBN/VBI Interpretation
1 cSt 3.97 Very low viscosity
10 cSt 23.53 Light oil range
100 cSt 33.92 Higher viscosity oil
1,000 cSt 39.01 Very viscous fluid

Refutas Equation Examples

Example 1: Convert kinematic viscosity to VBN

You have a kinematic viscosity of 100 cSt.

VBN = 14.534 \ln(\ln(100 + 0.8)) + 10.975
VBN \approx 33.92

The viscosity blending number is about 33.92.

Example 2: Convert VBN to kinematic viscosity

You have a VBN of 23.53.

\nu = e^{e^{(23.53 - 10.975)/14.534}} - 0.8
\nu \approx 10.00 \text{ cSt}

The kinematic viscosity is about 10 cSt.

Refutas Equation Calculator FAQ

What is the Refutas equation used for?

The Refutas equation is used to transform kinematic viscosity into a viscosity blending number. This is useful because viscosity does not blend linearly. The transformed VBN values can be used in blending calculations more easily than raw viscosity values.

Is VBN the same as VBI?

In this context, VBN and VBI refer to the same type of Refutas viscosity blending value. Both are dimensionless values calculated from kinematic viscosity.

Why must viscosity be greater than 0.2 cSt?

The equation contains ln(ln(ν + 0.8)). For this to be valid, the inside logarithm must be positive. That requires ν + 0.8 > 1, so ν > 0.2 cSt.