Weyl's formula states that:
$$N(R)=\frac{V+o(1)}{(4\pi)^{d/2}\Gamma\left(\frac d2+1\right)}R^{d/2},$$$$N(R)=\frac{1}{(4{\cdot}\pi)^{d/2}{\cdot}\Gamma\left(\frac d2+1\right)}{\cdot}V{\cdot}R^{d/2}+o(R^{d/2}).$$ where $d$ is the--- dimension, $V$ is the--- volume, and $N(R)$ is--- number of eigenvalues $\le R$. It works for any compact Riemannian manifold (and many noncompact ones as well).