Spindle nut for a ball screw, comprising a substantially hollow cylindrical workpiece of metal having an outer circumferential surface (M A) and a centrally symmetrical central longitudinal axis; having a ball groove which is arranged in a thread-like manner on the inner cylindrical surface and is designed to receive balls of diameter d, wherein an inner cylindrical surface is defined by the helical thread base line of the ball groove; further having rectilinear, substantially cylindrical relief bores, each provided in pairs, which are designed as inlet and outlet channels for the balls from and into the ball channel through the spindle nut wall, wherein each relief bore is characterized by - a generatrix having a point of intersection with the thread base line of the ball channel and representing the continuation of the path of a ball from the ball channel into the relief bore; and - a tangent to the cylinder surface which is parallel at a distance a to the generatrix, wherein both the tangent and the generatrix are perpendicular to a common perpendicular to the central longitudinal axis; wherein 1/5 d<a< 1/3 d applies for the distance a; and at the same time - both the tangent and the generatrix are perpendicular to a plane defined by the central longitudinal axis of the spindle nut and the perpendicular; characterized in that the running path of the ball in the ball groove is lowered on a running length l before the point of intersection of the ball groove with the generatrix such that the radial distance of the ball increases by t when passing l from the center axis, wherein 2/5 d<f<2/3 d applies to l. having a ball groove which is arranged in a thread-like manner on the inner cylindrical surface and is designed to receive balls of diameter d, wherein an inner cylindrical surface is defined by the helical thread base line of the ball groove; further having rectilinear, substantially cylindrical relief bores, each provided in pairs, which are designed as inlet and outlet channels for the balls from and into the ball channel through the spindle nut wall, wherein each relief bore is characterized by - a generatrix having a point of intersection with the thread base line of the ball channel and representing the continuation of the path of a ball from the ball channel into the relief bore; and - a tangent to the cylinder surface which is parallel at a distance a to the generatrix, wherein both the tangent and the generatrix are perpendicular to a common perpendicular to the central longitudinal axis; wherein 1/5 d<a< 1/3 d applies for the distance a; and at the same time - both the tangent and the generatrix are perpendicular to a plane defined by the central longitudinal axis of the spindle nut and the perpendicular; - a generatrix having a point of intersection with the thread base line of the ball channel and representing the continuation of the path of a ball from the ball channel into the relief bore; and - a tangent to the cylinder surface which is parallel at a distance a to the generatrix, wherein both the tangent and the generatrix are perpendicular to a common perpendicular to the central longitudinal axis; wherein 1/5 d<a< 1/3 d applies for the distance a; and at the same time - both the tangent and the generatrix are perpendicular to a plane defined by the central longitudinal axis of the spindle nut and the perpendicular; characterized in that the running path of the ball in the ball groove is lowered on a running length l before the point of intersection of the ball groove with the generatrix such that the radial distance of the ball increases by t when passing l from the center axis, wherein 2/5 d<f<2/3 d applies to l.