  It is well known that the angles in a lattice acting on hyperbolic $n$-space
become equidistributed. In this paper we determine a formula for the pair
correlation density for angles in such hyperbolic lattices. Using this formula
we determine, among other things, the asymptotic behavior of the density
function in both the small and large variable limits. This extends earlier
results by Boca, Pasol, Popa and Zaharescu and Kelmer and Kontorovich in
dimension 2 to general dimension $n$. Our proofs use the decay of matrix
coefficients together with a number of careful estimates, and lead to effective
results with explicit rates.
