This isn't my normal area of engineering, and I'm pulling from school memory, text books on my desk, and google. That said...
It may be possible that there isn't really a meaningful equivalent of the two. Brinell seems suited, much like Rockwell B and C, to harder materials.
The Brinell test has a nice well defined equation (rather than typing it out from my textbook, here's a link contained in DasRonin's link
http://www.engineersedge.com/manufacturing/brinell_hardness_test_equation_13173.htm).
However, my textbook gives the Equation for Rockwell hardness as:
R = C1 -C2*t
Where R is Rockwell harness, t is the depth of penetration, and C1 and C2 are constants that are defined based on the scale of Rockwell hardness that you are using (R in this case). However, I am unable to locate any information telling me just what these coefficients are for R, just that this scale is used for much softer materials such as polymers or soft metals.
I did note this from the University of Buffalo's Civil Engineering resources website (
http://civil.eng.buffalo.edu/cie616/2-LECTURES/Lecture%204a%20-%20Material%20Testing/HARDNESS%20TEST.pdf)
Hardness Conversion or Equivalents:
Hardness conversion between different methods and scales cannot be made
mathematically exact for a wide range of materials. Different loads, different shape of
indeters, homogeneity of specimen, cold working properties and elastic properties all
complicate the problem. All tables and charts should be considered as giving approximate
equivalents, particularly when converting to a method or scale which is not physically
possible for the particular test material and thus cannot be verified. An example would be
converting HV/10 or HR-15N value on a thin coating to the HRC equivalent.
View Quote
Which furthers my theory that they (Rockwell R and Brinell) may not be compatible/relate-able scales. It's worth noting that my textbook also goes into detail that their "conversion table" between Brinell and Rockwell C and B that is shown in the book is only valid for steels. Considering that the values are definable for one material but do not have corresponding values for another also lends credence to this.
I hope that helps, but I have a feeling it doesn't.
For morbid curiosity, what is the material and why is it needed to convert between the units?