The statistical-mechanical entropies of the Schwarzschild black hole arising from the scalar, Weyl neutrino, electromagnetic, Rarita-Schwinger and gravitational fields are investigated in the Painlevé and Leaitre coordinates.Although the metrics in the Painlevé and the Lemaitre coordinates do not obviously possess the singularity as that in the Schwarzschild coordinate, we find that the entropies of the arbitrary spin fields in both the Painlevé and Lemaitre coordinates are exactly equivalent to that in the Schwarzschild coordinate.