What is the maximum altitude at which a Cessna 172 can fly?
The absolute ceiling, or the maximum height an aircraft can fly to, is usually not published; manufacturers usually use service ceiling as the benchmark. Service ceiling is the maximum altitude which the aircraft can attain flying in air at Standard Temperature and Pressure (29.92" Hg and 15° C at MSL) and still be able to climb at a rate of at least 100 feet/min.
Depending on the model 172, this is between 13,000-15,000 feet ASL. A Cessna 172SP has a published service ceiling of 14,000 feet ASL.
Again whether an airplane can attain these altitudes on any given day is dependent on the condition of the air. The aircraft may be able to ascend higher than this on days when the air is very cold and there is a high local barometric pressure or lower on days when the air is warm and/or at a low barometric pressure in the region.
In September of 2007 in my 0-360 1959 172 I attained 18,003 ft GPS above 19AZ. I checked with Cessna customer service. The fella called me back a couple of days later. As far as he could find I did set a record. The plane was still climbing slowly and rather wobbly. I was happy to roll out and level off at 15 000 ft where I could catch my breath. I took off with a little less than half gas.
According to this, the 172's absolute ceiling (the altitude above which it is impossible to fly under standard meteorological conditions) is 15,000 feet.