The scope of the specific study is the extraction of mathematical relations which correlate the nominal capacity with capacity range of an inverter air conditioner unit with variable speed compressor under standard conditions, that is, measurements of minimum and maximum power of air conditioner under specific indoor and outdoor temperatures. Initially, the necessary statistical information for nominal minimum and maximum capacity will be collected from a sample of 544 different inverter air conditioner models. Furthermore, the regression analysis and the change curves of capacity range with regard to the nominal capacity for cooling and heating operation will be drawn. Also the change of turndown ratio with regard to the nominal capacity and capacity range of air conditioners will be studied. The conclusion that arises is that the maximum capacity and capacity range are varied linearly for cooling and heating operation. There is no clear indication for turndown ratio due to low correlation coefficient of the mathematical model.