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 Tcor ∼ 106.2 K, with no significant amount of material above T ∼ 106.8 K; the characteristic density is ne ∼ 3 x 109 cm-3 the emission measure is EM ∼ 4.5 × 1050 cm-3. We infer a (visible) volume of Vtot ∼ 5 x 1031 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 ∼ 2 x 109 cm and cover about 20% of the stellar surface. Because of the high coronal density and the lack of emission measure substantially below T ∼ 106 K, we conclude also that it is unlikely that there exists a cooler, acoustically heated subcorona.