How to find the h-index of a professor?
There is no such thing as "the precise h-index".

The h-index is defined as the largest integer h such that at least h of the author's publications have at least h citations each.  But what's a publication?  Do first-author publications carry more weight?  Do ArXiv, technical report, conference, and journal versions of the "same" paper (all of which may have citations) count as four papers or one?  Or does it depend on the difference in content between versions?  (How do you measure that difference?)  Does the quality of the venue matter?  If so, which venues count as "real" publications?  Do survey articles count?  Popular science articles?  Blog posts?  StackExchange questions?*  Do self-citations count?  If so, does a citation to a paper by X and Y, in a paper by Y and Z, count toward X's h-index?  How much (and who) are you willing to pay to make sure you've really counted every citation to every publication?

The different sources of the h-index make different well-reasoned decisions about each of these issues, none of which make sense for ALL areas, even within computer science.


  I think h-index is a better metric than the number of publications alone.


This is a pretty low standard.  You can do better.



*At least one of my StackExchange questions has more citations than at least one of my papers.