[Weyl's formula][1]:

$$N(R)=\frac{1}{(4{\cdot}\pi)^{d/2}\Gamma\left(\frac d2+1\right)}{\cdot}V{\cdot}R^{d/2}+o(R^{d/2}).$$
where $d$ --- dimension, $V$ --- volume, $N(R)$ --- number of eigenvalues $\le R$.
It works for any compact Riemannian manifold.


  [1]: http://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum#Weyl.27s_formula