Did you happen to delete the calculator from your apps on the phone? Can you find the calculator on the phone itself? If you find it, then try a reset. Hold the sleep/wake and home buttons together until you see the Apple logo and then release. The phone will reboot. There are no settings for changing what appears on the Control Center. See if the reset corrects your issue.
EDIT: What exactly are you seeing in Control Center? If you are just seeing the music controls, then swipe to the right to see the rest of the Control Center access.