  We assess the validity of the free magnetic energy - relative magnetic
helicity diagram for solar magnetic structures. We used two different methods
of calculating the free magnetic energy and the relative magnetic helicity
budgets: a classical, volume-calculation nonlinear force-free (NLFF) method
applied to finite coronal magnetic structures and a surface-calculation NLFF
derivation that relies on a single photospheric or chromospheric vector
magnetogram. Both methods were applied to two different data sets, namely
synthetic active-region cases obtained by three-dimensional
magneto-hydrodynamic (MHD) simulations and observed active-region cases, which
include both eruptive and noneruptive magnetic structures. The derived
energy--helicity diagram shows a consistent monotonic scaling between relative
helicity and free energy with a scaling index 0.84$\pm$0.05 for both data sets
and calculation methods. It also confirms the segregation between noneruptive
and eruptive active regions and the existence of thresholds in both free energy
and relative helicity for active regions to enter eruptive territory. We
consider the previously reported energy-helicity diagram of solar magnetic
structures as adequately validated and envision a significant role of the
uncovered scaling in future studies of solar magnetism.
