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We demonstrate that the vertical Lorentz force and a corresponding lower limit of the cross-field electric current density can be calculated from vector magnetograms of solar active regions obtained at a single height in the solar atmosphere, provided that the vertical gradient of the magnetic field strength is known at this height. We use a predicted vertical magnetic field gradient derived from a previous analysis. By testing various force-free solutions, we find that the numerical accuracy of our method is satisfactory. Applying the method to active region photo- spheric vector magnetograms, we find vertical Lorentz forces ranging from several hundredths to a few tenths of thetypicalphotosphericgravitationalforce,andtypicalcross-fieldcurrentdensitiesuptoseveraltimes10mAm  2 . The typical vertical current density is found to be 2-3 times smaller, on the order of 10-15 mA m  2 .T hese differences are above the associated uncertainties. The values of the cross-field currents decrease in an averaged vector magnetogram, but the ratio of the cross-field to the vertical current density increases, also above the uncertainties. We conclude that the photospheric active region magnetic fields are not force-free, contrary to the conjectures of some recent studies. Subject heading

Vertical Lorentz Force and Cross‐Field Currents in the Photospheric Magnetic Fields of Solar Active Regions