The Molière radius is a characteristic constant of a material giving the scale of the transverse dimension of the fully contained electromagnetic showers initiated by an incident high energy electron or photon. By definition, it is the radius of a cylinder containing on average 90% of the shower's energy deposition. Two Molière radii contain 95% of the shower's energy deposition. It is related to the radiation length X 0 by the approximate relation R M = 0.0265 X 0 (Z + 1.2), where Z is the atomic number. The Molière radius is useful in experimental particle physics in the design of calorimeters : a smaller Molière radius means better shower position resolution, and better shower separation due to a smaller degree of shower overlaps.