The absolute flux of cosmic-ray electrons has been measured using a balloon-borne superconducting magnet spectrometer. The instrument consisted of a gas Cerenkov detector, a momentum spectrometer, and a lead-scintillator shower counter. The flux of electrons in the interstellar medium was determined by correcting the observed flux for energy loss in the atmosphere and the payload and for solar modulation. The flight was made at an average atmospheric depth of 5.8 g cm/sup -2/, and the solar modulation was taken to be 300 MeV. The flux in the interstellar medium was found to be 367E/sup() -3.15plus-or-minus0.2/ e/sup -/ m/sup -2/ sr/sup -1/ s/sup -1/ GeV/sup -1/ in the energy interval 4.5-63.5 GeV. The uncertainty in the absolute flux is 10%. The result has been validated by the use of data from a second balloon flight, the use of alternate selection criteria, and simultaneous measurement of other absolute fluxes.