The relationship between the determination of the circumference of the Earth and the geographical mapping performed by Ptolemy in his Geography is discussed. A simple transformation of the Ptolemaic coordinates to the circumference of the Earth measured by Eratosthenes, based on the assumption that the metrical values of the stadion used by both Ptolemy and Eratosthenes are equivalent, drastically improves the positions of the locations given in Ptolemy’s catalogue at least for a great part of the oikoumenē. Comparing the recalculated positions of the identified localities with their actual positions, it turns out that the distances extracted by Ptolemy from ancient sources are remarkably precise. This in turn confirms the high precision of Eratosthenes’s result for the circumference of the Earth. It is shown that many distortions of Ptolemy’s world map can be explained as pure mathematical consequences of a mapping onto the surface of a sphere of wrong size.