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We provide completely effective error estimates for Stirling numbers of thefirst and second kind, denoted by $s(n,m)$ and $S(n,m)$, respectively. Thesebounds are useful for values of $m \geq n - O(\sqrt{n})$. An application of ourTheorem 5 yields, for example, \[ s(10^{12},\ 10^{12}-2\times10^6)/10^{35664464} \in [ 1.87669, 1.876982 ], \] \[ S(10^{12},\10^{12}-2\times 10^6)/10^{35664463} \in [ 1.30121, 1.306975 ]. \] The boundsare obtained via Chen-Stein Poisson approximation, using an interpretation ofStirling numbers as the number of ways of placing non-attacking rooks on achess board.  As a corollary to Theorem 5, summarized in Proposition 1, we obtain twosimple and explicit asymptotic formulas, one for each of $s(n,m)$ and $S(n,m)$,for the parametrization $m = n - t\, n^a$, $0 \leq a \leq \frac{1}{2}.$ Theseasymptotic formulas agree with the ones originally observed by Moser and Wymanin the range $0<a<\frac{1}{2}$, and they connect with a recent asymptoticexpansion by Louchard for $\frac{1}{2}<a < 1$, hence filling the gap at $a =\frac{1}{2}$.  We also provide a generalization applicable to rook and file numbers.

Completely effective error bounds for Stirling Numbers of the first and second kind via Poisson Approximation