Aims. Estimating Alfvén speeds is of interest in modelling the solar corona, studying the coronal heating problem and understanding the initiation and propagation of coronal mass ejections (CMEs). Methods. We assume here that the corona is in a magnetohydrostatic equilibrium and that, because of the low plasma $\beta$, one may decouple the magnetic forces from pressure and gravity. The magnetic field is then described by a force-free field for which we perform a statistical study of the magnetic field strength with height for four different active regions. The plasma along each field line is assumed to be in a hydrostatic equilibrium. As a first approximation, the coronal plasma is assumed to be isothermal with a constant or varying gravity with height. We study a bipolar magnetic field with a ring distribution of currents, and apply this method to four active regions associated with different eruptive events. Results. By studying the global properties of the magnetic field strength above active regions, we conclude that (i) most of the magnetic flux is localized within 50 Mm of the photosphere; (ii) most of the energy is stored in the corona below 150 Mm; (iii) most of the magnetic field strength decays with height for a nonlinear force-free field slower than for a potential field. The Alfvén speed values in an isothermal atmosphere can vary by two orders of magnitude (up to 100 000 km s-1). The global properties of the Alfvén speed are sensitive to the nature of the magnetic configuration. For an active region with highly twisted flux tubes, the Alfvén speed is significantly increased at the typical height of the twisted flux bundles; in flaring regions, the average Alfvén speeds are above 5000 km s-1 and depart highly from potential field values. Conclusions. We discuss the implications of this model for the reconnection rate and inflow speed, the coronal plasma beta and the Alfvén transit time.