Rotational invariance is a fundamental aspect of symmetry in scattering processes from atomic potentials. Here, we introduce a new approach for measuring orbital angular momentum (OAM), a key descriptor of rotational symmetry, during measurements of atomic transitions. We use an electron optical ‘OAM sorter’in combination with electron energy-loss spectroscopy (EELS) to perform a unified spectral analysis of the π* and σ* anti-bonding transitions in hexagonal boron nitride on the atomic scale. The approach allows multipolar transitions that are not accessible using conventional linear momentum-resolved EELS to be separated. It also offers prospects for greater efficiency in measurements of magnetic chiral dichroism.