Trivalent erbium Er3+ (4f11), as a dopant in the laser host material Y3 Al5 O12 (YAG), is a well-known and popular activator ion in a medium having optical, thermal, and mechanical properties suitable for numerous photonic applications. Despite its technological importance, a detailed intensity analysis of transitions between individual Stark components has not previously been attempted. This work presents an intensity analysis for Er:YAG, achieving good agreement between measured and calculated Stark-component transition intensities. Ambiguities in the parametrization due to different possible orientations of the quantization axes are addressed. Use of the “vector crystal field” parametrization resolves additional ambiguities that arise in the transition intensity parameters for low symmetry systems, and allows for a new definition for polarization-resolved Judd-Ofelt parameters, which can have wide-ranging applicability for polarized multiplet-to-multiplet intensity calculations.