  We self-consistently derive the magnetic energy and relative magnetic
helicity budgets of a three-dimensional linear force-free magnetic structure
rooted in a lower boundary plane. For the potential magnetic energy we derive a
general expression that gives results practically equivalent to those of the
magnetic Virial theorem. All magnetic energy and helicity budgets are
formulated in terms of surface integrals applied to the lower boundary, thus
avoiding computationally intensive three-dimensional magnetic field
extrapolations. We analytically and numerically connect our derivations with
classical expressions for the magnetic energy and helicity, thus presenting a
so-far lacking unified treatment of the energy/helicity budgets in the
constant-alpha approximation. Applying our derivations to photospheric vector
magnetograms of an eruptive and a noneruptive solar active regions, we find
that the most profound quantitative difference between these regions lies in
the estimated free magnetic energy and relative magnetic helicity budgets. If
this result is verified with a large number of active regions, it will advance
our understanding of solar eruptive phenomena. We also find that the
constant-alpha approximation gives rise to large uncertainties in the
calculation of the free magnetic energy and the relative magnetic helicity.
Therefore, care must be exercised when this approximation is applied to
photospheric magnetic field observations. Despite its shortcomings, the
constant-alpha approximation is adopted here because this study will form the
basis of a comprehensive nonlinear force-free description of the energetics and
helicity in the active-region solar corona, which is our ultimate objective.
