Door drive for a door, having a housing with a hydraulic cylinder, a drive mechanism which is able to be coupled to the door and is disposed in the hydraulic cylinder and has a displaceable drive piston and a closer spring which impinges the drive piston in the closing direction of the door, wherein formed on the side of the drive piston that lies opposite the closer spring is a pressure chamber for impinging the drive piston with a hydraulic fluid in the opening direction of the door, a hydraulic system, and a hydraulic pump for conveying the hydraulic fluid to the pressure chamber, wherein the hydraulic pump is designed as a piston pump having a pump piston which is axially displaceable and co-rotationally disposed in a fluid chamber and is sealed in relation to a wall of the fluid chamber and delimits a pump chamber which is connected to the pressure side of the hydraulic pump, wherein the hydraulic system has a first hydraulic connection which connects the pump chamber to the pressure chamber, wherein the hydraulic pump comprises an electric motor unit having a drive shaft, and a drive portion of the drive shaft is coupled to the pump piston via a threaded connection in order to axially displace the pump piston in the fluid chamber and thereby perform a stroke of the pump piston, wherein the hydraulic system has a second hydraulic connection which connects the pressure chamber to a spring chamber in which the closer spring is disposed, wherein in the second hydraulic connection there is an electrically switchable shut-off valve for selectively releasing or preventing a flow from the pressure chamber into the spring chamber and thus for moving the drive piston in the closing direction, characterized in that the fluid chamber and the spring chamber are separated by a disc element, wherein the disc element has a sleeve which is closed towards the spring chamber and extends into the spring chamber and encloses a sleeve chamber, wherein the sleeve chamber is contiguous to the fluid chamber without walls, thus enlarging the fluid chamber by the sleeve chamber, wherein the seal of the pump piston in relation to the wall of the fluid chamber is disposed on an end of the pump piston facing the motor unit, and a portion of the pump piston extends at least temporarily into the sleeve chamber during the operation of the hydraulic pump. a drive mechanism which is able to be coupled to the door and is disposed in the hydraulic cylinder and has a displaceable drive piston and a closer spring which impinges the drive piston in the closing direction of the door, wherein formed on the side of the drive piston that lies opposite the closer spring is a pressure chamber for impinging the drive piston with a hydraulic fluid in the opening direction of the door, a hydraulic system, and a hydraulic pump for conveying the hydraulic fluid to the pressure chamber, wherein the hydraulic pump is designed as a piston pump having a pump piston which is axially displaceable and co-rotationally disposed in a fluid chamber and is sealed in relation to a wall of the fluid chamber and delimits a pump chamber which is connected to the pressure side of the hydraulic pump, wherein the hydraulic system has a first hydraulic connection which connects the pump chamber to the pressure chamber, wherein the hydraulic pump comprises an electric motor unit having a drive shaft, and a drive portion of the drive shaft is coupled to the pump piston via a threaded connection in order to axially displace the pump piston in the fluid chamber and thereby perform a stroke of the pump piston, wherein the hydraulic system has a second hydraulic connection which connects the pressure chamber to a spring chamber in which the closer spring is disposed, wherein in the second hydraulic connection there is an electrically switchable shut-off valve for selectively releasing or preventing a flow from the pressure chamber into the spring chamber and thus for moving the drive piston in the closing direction, characterized in that the fluid chamber and the spring chamber are separated by a disc element, wherein the disc element has a sleeve which is closed towards the spring chamber and extends into the spring chamber and encloses a sleeve chamber, wherein the sleeve chamber is contiguous to the fluid chamber without walls, thus enlarging the fluid chamber by the sleeve chamber, wherein the seal of the pump piston in relation to the wall of the fluid chamber is disposed on an end of the pump piston facing the motor unit, and a portion of the pump piston extends at least temporarily into the sleeve chamber during the operation of the hydraulic pump.