A position determining device is equipped with a matching unit. The matching unit matches a random pattern in a photographed image of a portion of a ceiling or floor photographed by a portable terminal against a random pattern in a photographed image of a larger area of the ceiling or floor than the aforementioned portion so as to determine the position of the photographed image of the aforementioned portion on the photographed image of the larger area. The matching unit determines the position of the ceiling located above the portable terminal or the position of the floor located therebelow on the basis of the identified position on the photographed image of the larger area.