Summary: In a previous article [A. Hammett, Coll. Math. J. 51, No. 5, 330–336 (2020; Zbl 1473.97026)] appearing in this journal, existence of the finite positive limit \(\kappa = \lim_{n\to\infty} n!(\frac{e}{n})^nn^{-1/2}\) implicit in Stirling’s approximation \(n! \approx \sqrt{2\pi n}(\frac{n}{e})^n\) was proved, and in so doing this limit was connected to the Euler limit \(\lim_{n\to\infty}(1 + \frac{1}{n})^n = e\). Because it was not done in the original article, exact determination of the constant \(\kappa\) (\(= \sqrt{2\pi}\)) by a novel, elementary technique is the aim of this follow-up. For both articles, the arguments are readily accessible to advanced undergraduate students with a year of university calculus in their background.