An electrical machine has a rotor with a hollow shaft which in its interior delimits a hollow shaft axial channel that extends in the axial direction and into which a cooling fluid can flow during operation of the electrical machine. A laminated rotor core is fitted radially to the outside of the hollow shaft and has two axial end sides. An axial channel which is delimited by the laminated rotor core extends in the axial direction from one of the two end sides of the laminated rotor core to the other of the two end sides of the laminated rotor core and is connected in a fluid-conducting manner to the hollow shaft axial channel, so that, during operation of the electrical machine, the cooling fluid can flow from the hollow shaft axial channel to the end sides via the axial channel and can flow radially to the outside downstream of the axial channel owing to centrifugal force.