Integral relations for the average poloidal beta p and the plasma internal inductance ℓi are derived from the magnetohydrodynamic (MHD) equilibrium equation for an axisymmetric torus. The volume-dependent parameters that appear depend only weakly on the actual current density distribution inside the plasma and can be evaluated approximately, given the plasma shape and boundary poloidal magnetic field. In practice, these can be accurately and efficiently obtained for both diverted and limited plasmas from measured external poloidal magnetic field and flux values by approximating the plasma current distribution using a few filaments or distributed sources. For a tokamak plasma with a non-circular cross-section of sufficient elongation, p and ℓi can then be approximately determined separately. This is demonstrated for analytic equilibria of known shape as well as for actual Doublet III (D-III) plasmas for which p and ℓi have been determined by using other methods. Results of a sensitivity study are described.