An electric machine having a stator arranged in a machine housing and a rotor mounted rotatably relative to the stator about an axis of rotation, wherein the machine housing includes at least one coolant inlet port for supplying coolant to the machine housing and at least one coolant outlet port for draining coolant from the machine housing. It is provided that the coolant inlet port empties into a distribution annulus and several housing coolant ducts emerge from the distribution annulus and extend beyond the stator, when viewed in the axial direction, and are connected fluidically, on their side facing away from the distribution annulus, to stator cooling duct inlets of stator cooling ducts formed in the stator, which pass entirely through the stator in the axial direction.