In the process of Solar wind Magnetosphere Ionosphere (SW-M-I) system there is a resulting energy rate being dissipated in the ionosphere. One of this is joule heating which causes some thermal expansion in the ionosphere. Here the joule heating was computed using some empirical relations, Auroral electrojet indices are used as input to the relation. Hourly provisional data values were obtain for the year 2010, 2011,2012,and 2013 were obtain at ISGI from world date center Kyoto and International Association for Geomagnetism and Aeronomy (IAGA) 2002 format was adopted during the computation under the assumption that the magnetosphere those not store any power. The coefficient of determination of this relations where compared and it was found the Baumjohann and Kamide relation has a better coefficient of determination which shows that they accurately estimate this energy rate compare to other relations.