Plumbing fixtures with a valve actuator for automatically controlling pivoting of a flush valve, and methods of calibrating movement of the flush valve, are disclosed. The motor of the valve actuator may be positioned between the bowl of the fixture and a leg of a trapway to provide compact assembly. A belt drive laterally extending along the trapway links the motor to the flush valve. The method of calibrating includes establishing stop points which are at positions of less resistance than hard stop positions.