An arc furnace for quickly and continuously melting directly reduced iron ore so as to make steel, wherein the furnace wall above the hearth line and the furnace roof have partly spherical inner surfaces, the spherical surface defining these inner surfaces having the center located adjacent to the point equidistantly spaced apart from the lower ends of electrodes, and the electrodes are inclined at an angle to the vertical so that the distance between the lower ends thereof may be reduced to a minimum.