Some cats calmly stroll out of a litter box after using it, but other cats run around like a nut. One reason why cats may run like crazy after using a litter box stems from their past when they would relieve themselves and then run back to their lair.
Another explanation is that relieving themselves stimulates the cat to feel happy (much like many humans) so then they want to run around in joy. Still another reason is that cats may hate the smell of their own litter and want to get as far away from it as possible.
Whatever the real reason for your cat, chances are your cat’s behavior will simply puzzle you for the rest of your life.