A cooling device for a stator of an electrical machine, for fitting together with a hollow cylindrical laminated core of the stator, includes multiple cooling channels for conducting cooling fluid along the laminated core, and a fluid ring for provision on an end face of the laminated core. The fluid ring has two fluid ring channels for distributing the cooling fluid to the cooling channels and for receiving the cooling fluid from the cooling channels, and at least two cooling fluid connections for introducing and removing the cooling fluid into and from the fluid ring channels. The fluid ring channels have circumferential-angle-dependent flow cross-sections in the flow direction, in order to evenly distribute the cooling fluid to the cooling channels.