How long does it take for appendicitis to move from the belly to the right side?

Less than 24 hrs. The 'classic' presentation of appendicitis is of cramping upper or mid abdominal pain which moves to the right lower abdomen, changing in character to a sharp, well-localized, progressively-worsening pain. This change in location and character of pain typically occurs 12-24 hours after the onset of symptoms. Keep in mind: not everyone has this initial pain.
Within 24 hours. Appendicitis usually presents with poorly-localizing periumbilical pain, nausea, vomiting, and low grade fever. Within 24 hours, it is typical for the pain to localize to the rlq. This pain may be associated with peritoneal signs on physical examination. For patients whose appendix is not located in the rlq (i.e., retrocecal or pelvic position), the pain may never localize to the rlq.