I too am related to the king being his sixth cousin 16 times removed.
My connection with the Plantagenet monarch is through King Henry III and this makes me even more distant than Mr Cumberbatch. It has been estimated that between one million and seventeen million people are related in some way to Richard III but as Dr Turi King from the University of Leicester points out we are all related to Richard, "it’s simply a matter of degree. What makes Cumberbatch different in this case" says Dr King, "is that how he is related to Richard is known." Cumberbatch is related to Richard III through Edward III, Henry III's great-grandson.
However distant, it is nonetheless, a connection, and that is why researching your family tree is such a rewarding hobby. Even if you don't find your royal ancestor you will certainly learn an awful lot of about history along the way.
Here is what I have learnt.
Also, here is a word of advice, don't be put off