An electronic device may be provided with electronic components such as mapping circuitry for measuring distances, areas, volumes or other properties of objects in the surrounding environment of the device. The mapping circuitry may include a laser sensor and device position detection circuitry. The device may include processing circuitry configured to gather laser sample data and device position data using the laser sensor and the device position detection circuitry. The laser sample data and the device position data may be gathered while pointing a laser beam generated with a laser in the laser sensor at one or more sample points on a surface such as a surface of a wall. By tracking the device position and orientation using the device position detection circuitry, the objects may be mapped while gathering laser sample data from any position with respect to the object.