Rotor shaft (1; 10) for a wind turbine, comprising - a flange for acceptance of a hub of a rotor of a wind turbine, - an output side for the derivation of a rotation movement, especially into a gear box, - a shaft and an intermediate section, - in which the flange passes over the intermediate section into the shaft - and the shaft is connected with the output side, - in which the rotor shaft (1; 10) is substantially hollow, - and in which the shaft comprises a bearing surface on the outer surface for the support on a main bearing of the wind turbine, - in which the bearing surface is spaced apart in an axial direction with an effective bearing clearance from the flange surface and arranged on an area of the shaft bordering the intermediate section, - the rotor shaft (1; 10) substantially consists of a metallic casting material and - features an inner surface located inside and frontally in one radial direction and one outer surface located outside, - in which the inner surface of the intermediate section is designed convexly curved in one section plane defined by a radial direction and axial direction with at least one inner radius (R i0; R i1, R i2), - the outer section of the intermediate section in the section plane is formed concavely curved with at least one outer radius (R a1, R a2), - the outer section and the inner section of the intermediate section are substantially designed continuously proceeding, and - the intermediate section is geometrically formed in a way that a maximum tension at each point of the rotor shaft (1; 10) always lies under the yield strength (R p, 0, 2) defined for the casting material, - in which the maximum tension is calculated with the help of a load profile stated for the permission of the rotor shaft (1; 10) and - in which the rotor shaft furthermore comprises a ring symmetrically in axial direction formed protrusion (20; 40) for the support of the flange, whereas the protrusion (20; 40) is located on a front side of the rotor shaft (1; 10) away from the output on the intermediate section and forms part of the inner section. - a flange for acceptance of a hub of a rotor of a wind turbine, - an output side for the derivation of a rotation movement, especially into a gear box, - a shaft and an intermediate section, - in which the flange passes over the intermediate section into the shaft - and the shaft is connected with the output side, - in which the rotor shaft (1; 10) is substantially hollow, - and in which the shaft comprises a bearing surface on the outer surface for the support on a main bearing of the wind turbine, - in which the bearing surface is spaced apart in an axial direction with an effective bearing clearance from the flange surface and arranged on an area of the shaft bordering the intermediate section, - the rotor shaft (1; 10) substantially consists of a metallic casting material and - features an inner surface located inside and frontally in one radial direction and one outer surface located outside, - in which the inner surface of the intermediate section is designed convexly curved in one section plane defined by a radial direction and axial direction with at least one inner radius (R i0; R i1, R i2), - the outer section of the intermediate section in the section plane is formed concavely curved with at least one outer radius (R a1, R a2), - the outer section and the inner section of the intermediate section are substantially designed continuously proceeding, and - the intermediate section is geometrically formed in a way that a maximum tension at each point of the rotor shaft (1; 10) always lies under the yield strength (R p, 0, 2) defined for the casting material, - in which the maximum tension is calculated with the help of a load profile stated for the permission of the rotor shaft (1; 10) and - in which the rotor shaft furthermore comprises a ring symmetrically in axial direction formed protrusion (20; 40) for the support of the flange, whereas the protrusion (20; 40) is located on a front side of the rotor shaft (1; 10) away from the output on the intermediate section and forms part of the inner section.