Disclosed is a cooling device for cooling a rotor 1, which is rotatably mounted about an axis of rotation 2, of an electric machine, wherein the rotor 1 is supported by a central rotor shaft 3 and comprises a hollow space 5 in the interior of the rotor shaft 3 for receiving coolant 6. The cooling device has at least one first coolant line 7a that extends radially outwardly from the hollow space 5 and a ring-shaped first distribution line 11a that is fluidically connected to the hollow space via the first coolant line 7a. Also disclosed are a rotor of an electric machine comprising such a cooling device and such an electric machine.