We demonstrate that the discrete dipolar sums can be separated into two contributions: thickness- and geometry-dependent parts. The geometry-dependent part is analogous to the shape dependence of the continuum approach. The correct normalization of the dipolar energy eliminates the apparent discrepancies of the discrete summation with the experimental results and continuum Maxwell theory. The superposition of the two contributions explains a new phenomenon, i.e. the size-dependent spin reorientation transition and/or enhancement of the effective perpendicular anisotropy.