When I convert video files into mp4, their size increases

Whenever I change a video file into an mp4, it's size increases 2-3 times, although I set it to the same bitrate. Shouldn't this keep the file size same, and not increase it unnecessarily?

Please help, I am running out of HDD space! :/

Oh, and I'm converting the videos to run on an Apple TV, so don't say use a different format.