On January 26, 2013, about 1800 Pacific standard time, a Cessna 152, N68757, experienced a loss of engine power while on approach for landing on runway 31 at Castle Airport (MER), Atwater, California. The pilot made a forced landing about 3 miles west of the airport in an open field; during the landing rollout, the airplane struck a culvert and nosed over, coming to rest inverted. The student pilot, the sole occupant, was not injured. Sierra Academy of Aeronautics operated the airplane under the provisions of 14 Code of Federal Regulations Part 91 as an instructional flight. The airplane sustained substantial damage to the tail section and wings. Visual meteorological conditions prevailed for the local area flight, and no flight plan had been filed. The flight departed from MER about 1600.The student pilot was interviewed by an inspector from the Federal Aviation Administration (FAA). The student pilot reported that he arrived at the airport at 1530 for a 1600 flight. In preparation for his flight, he checked the local weather, and calculated the airplane's weight and balance, which included full fuel. During the preflight inspection, he reported that the fuel tanks were not full; about 12 gallons of fuel were on board, and he needed a "bottle" of oil for the engine. The pilot reported that the flight was to be 1.3 hours long; no problems were encountered with the flight. About 10 minutes after starting toward MER, the pilot became lost and contacted NorCal approach (Northern California Terminal Radar Approach Control) for assistance. The student pilot reported that even though he was provided with position reports back to the airport, he was not able to identify the airport, until he was about 10 miles from the airport. At that point, the engine began to run rough; the student pilot added full power, and the engine ran normal for about 20 seconds and then stopped. The student pilot attempted to restart the engine; however, he was not able to. He trimmed the airplane for best glide speed, and flared before landing. During the landing rollout, the airplane impacted a small rise in the ground, and came to rest inverted. The flight school was given permission to recover the airplane to their facility. An interview with the chief pilot revealed that upon his arrival at the accident site, he noted no smell of fuel present and that the fuel tanks had not been compromised. Once the airplane was righted, he was able to drain a total of 1 gallon of fuel; 1/2 gallon from each wings' fuel tank. According to the flight school, all flights were grounded pending a safety meeting, in which they would reiterate that solo students should not depart for a flight with less than full fuel tanks, and solo students should not be dispatched with less than 3 hours of daylight remaining for a local flight. According to the 1978 Cessna pilot's operating handbook, the airplane has a total fuel capacity of 26.0 gallons; 24.5 gallons is useable, with a maximum of 1.5 gallons of unusable fuel. With full fuel, the range of the airplane would have been approximately 3.4 hours.