We derive the coronal density of the nearby star Procyon, using an observation with the short- and medium-wavelength spectrometers on board the Extreme-Ultraviolet Explorer satellite (EUVE). Specifically, we have identified density-sensitive ratios in lines due to iron in ionization stages Fe X to Fe XIV, which have been detected in our EUVE spectra. We present these observations and analyze these line ratios, paying careful attention to line blends or contamination from other extreme-ultraviolet (EUV) lines. We show that all the available density-sensitive iron line diagnostics are consistent with the interpretation that the overall coronal output of Procyon is dominated by regions with a coronal density very much resembling densities typically found in active regions on the Sun. We estimate that the corona of Procyon is dominated by material at a temperature T-cor similar to 10(6.2) K, With no significant amount of material above T similar to 10(6.8) K; the characteristic density is n(e) similar to 3 x 10(9) cm(-3); the emission measure is EM similar to 4.5 x 10(50) cm(-3). We infer a (visible) volume of V-tot similar to 5 x 10(31) cm(3); assuming the X-ray emission to arise from plasma magnetically confined in loops, we deduce that such loops have an average height of h similar to 2 x 10(9) cm and cover about 20% of the stellar surface. Because of the high coronal density and the lack of emission measure substantially below T similar to 10(6) K, we conclude also that it is unlikely that there exists a cooler, acoustically heated subcorona.