The average height of a two-story house varies based upon ceiling height. In general, a story is calculated as 10 feet. This accounts for 8-foot ceiling heights with a 2-foot allowance for the infrastructure of the roof, so a two-story house would be about 20 feet high.
Some houses feature higher ceilings, so they are naturally taller than 20 feet. Calculating stories, though, isn't always as simple as doubling the story height for the first floor of the home. Roof pitch and the height of the ceilings on the second floor, if they vary from the first, also affect the calculations. Some city ordinances, however, set a limit to the height of two-story houses for aesthetic purposes.