To be able to see your whole body you only need to keep in mind two factors. The bottom of a mirror can at most be at the midpoint between your eyes and your feet/floor. The top of the mirror only needs to be at the halfway point between your eyes and the top of your head.
Thus, you'll only ever need a mirror half as tall as you are in order to see your full body.
The same principle can be used to figure out the necessary width of the mirror.