Let $(M,psi)$ be a $(2n+1)$-dimensional oriented closed manifold equipped with a pseudo-free $S^1$-action $psi : S^1 times M rightarrow M$. We first define a textit{local data} $mathcal{L}(M,psi)$ of the action $psi$ which consists of pairs $(C, (p(C) ; overrightarrow{q}(C)))$ where $C$ is an exceptional orbit, $p(C)$ is the order of isotropy subgroup of $C$, and $overrightarrow{q}(C) in (Z_{p(C)}^{times})^n$ is a vector whose entries are the weights of the slice representation of $C$. In this paper, we give an explicit formula of the Chern number $langle c_1(E)^n, [M/S^1] rangle$ modulo $Z$ in terms of the local data, where $E = M times_{S^1} C$ is the associated complex line orbibundle over $M/S^1$.Also, we illustrate several applications to various problems arising in equivariant symplectic topology.