Apparatus for measuring the profile of a wellbore includes a cylindrical body having first and second ends threaded for connection in line with a drill string. A passage extends through the body between the first and second ends. A plurality of arms are pivotally coupled on an outer surface of the cylindrical body. Each of the arms is biased to pivot so as to move a free end thereof radially away from the outer surface of the body. The plurality of arms are angularly spaced apart around the cylindrical body and arranged in a plurality of tiers. Each of the tiers comprises three or more of the arms. The tiers are spaced apart axially from one another along the cylindrical body. Sensors are operable to directly or indirectly measure radial extension of each of the arms from the cylindrical body. A holding mechanism is operable to hold the arms in a retracted configuration and to selectively release the arms to pivot away from the cylindrical body. The arms may be extended while withdrawing a drill string containing the apparatus from a wellbore to monitor a profile of a wall of the wellbore.