A ball screw device comprising: a ball screw shaft with an outer circumferential ball rolling groove (23a1) formed spirally in an outer circumferential surface; a ball nut with an inner circumferential ball rolling groove (21a1) formed spirally in an inner circumferential surface, the outer circumferential ball rolling groove (23a1) and the inner circumferential ball rolling groove (21a1) forming a spiral track; a deflector that is provided in the ball nut and forms a coupling passage that crosses over a ridge between adjacent portions of the outer circumferential ball rolling groove (23a1); a plurality of rolling balls that are housed in array inside a circulation path formed by substantially one turn of the spiral track and the coupling passage; and a retainer that is disposed between the ball screw shaft and the ball nut and has a retainer groove in which the rolling balls are retained, wherein the coupling passage is defined by the outer circumferential ball rolling groove (23a1), the ridge between adjacent portions of the outer circumferential ball rolling groove (23a1), and a ceiling surface that is formed on the deflector and faces the outer circumferential ball rolling groove (23a1) and the ridge, and a top surface of the ridge has a shape of a cylindrical surface centered at a central axis of the ball screw shaft, characterized in that, the ceiling surface of the coupling passage has: a first rounded portion at which a projected shape of the ceiling surface seen in an axial direction of the ball screw shaft has a single first radius of curvature centered at the central axis of the ball screw shaft, such that a constant first clearance (α1) is provided between the rolling balls and the ceiling surface at least in a range in which the rolling balls are able to roll over the top surface of the ridge; and a second rounded portion at which the projected shape of the ceiling surface has a second radius of curvature smaller than the first radius of curvature wherein the second rounded portion is located more toward a groove bottom of the outer circumferential ball rolling groove (23a1) than the range where the first rounded portion is formed a ball screw shaft with an outer circumferential ball rolling groove (23a1) formed spirally in an outer circumferential surface; a ball nut with an inner circumferential ball rolling groove (21a1) formed spirally in an inner circumferential surface, the outer circumferential ball rolling groove (23a1) and the inner circumferential ball rolling groove (21a1) forming a spiral track; a deflector that is provided in the ball nut and forms a coupling passage that crosses over a ridge between adjacent portions of the outer circumferential ball rolling groove (23a1); a plurality of rolling balls that are housed in array inside a circulation path formed by substantially one turn of the spiral track and the coupling passage; and a retainer that is disposed between the ball screw shaft and the ball nut and has a retainer groove in which the rolling balls are retained, wherein the coupling passage is defined by the outer circumferential ball rolling groove (23a1), the ridge between adjacent portions of the outer circumferential ball rolling groove (23a1), and a ceiling surface that is formed on the deflector and faces the outer circumferential ball rolling groove (23a1) and the ridge, and a top surface of the ridge has a shape of a cylindrical surface centered at a central axis of the ball screw shaft, characterized in that, the ceiling surface of the coupling passage has: a first rounded portion at which a projected shape of the ceiling surface seen in an axial direction of the ball screw shaft has a single first radius of curvature centered at the central axis of the ball screw shaft, such that a constant first clearance (α1) is provided between the rolling balls and the ceiling surface at least in a range in which the rolling balls are able to roll over the top surface of the ridge; and a second rounded portion at which the projected shape of the ceiling surface has a second radius of curvature smaller than the first radius of curvature wherein the second rounded portion is located more toward a groove bottom of the outer circumferential ball rolling groove (23a1) than the range where the first rounded portion is formed