Thanks for the example.  I note that on the site you quote it says "*There is a small probability of one day error."  And a number of other sites have the same advisory (perhaps they are all using the same copied javascript algorithm behind the scenes).  And testing some of the sites one can put in invalid dates and still get an answer (e.g. April 31st which does not exist).  Mathematica of coruse sensibly gives an error message if you try to convert April 31.

In Mathematica (which presumably is the code behind the Wolfram|Alpha calculation) one gets

And it seems that this is probably the correct answer.  Note that other sites agree with this.  For example 

http://www.iacad.gov.ae/en/pages/hijritogregorian.aspx

and 

http://www.mela.us/committees/hegira.html

But the code behind these sites is only as good as what one sees (i.e., one needs to look at the Javascript source behind, for example, the last pate's link... easy enough to see if one "shows source" for the page).

here's the wikipedia article:

http://en.wikipedia.org/wiki/Islamic_calendar#Converting_Hijri_to_Gregorian_date_or_vice_versa

I actually don't know much about this subject, so take my links & c with grains of salt. 

As always, giving an example would help us folks who'd like to examine the problem and offer help...  ;-)