Lie algebra, maximal toral sub-algebra Is there a relation between number of roots of a finite dimensional semi-simple Lie algebra L and  dimension of the maximal toral sub-algebra H(Cartan sub-algebra) of L?

Thanks!
There is the relation
$$
\dim (H)+\mid \Phi\mid =\dim (L),
$$
where $\mid \Phi\mid$ denotes the cardinality of the root system of $L$. For example, with $L$ of type $A_n$ we have $\dim (H)=n$, $\mid \Phi\mid=n^2+n$ and $\dim(L)=n^2+2n$.
With notations as in the question,
2 dim(H) &lt;= no. of roots.
This is true because roots span H*(Dual space of H) and roots always occur in pairs.(I mean x is a root iff -x is a root.)  

I do not hope there is any other relation, in general. But, may be, if we consider some special classes of L, we may have some better results!