Does my calendar back up automatically to iCloud

Are you using the iCloud calendar, or just the calendar app on the iPhone? If you are using iCloud calendar, iCloud backs up its own content, but it is not in your iPhone backup. If you backup via iCloud or iTunes, all you do is turn on iCloud calendar in Settings and your content is there. When you backup your iPhone in iCloud, it does not backup content that is already in iCloud. If you are using the calendar app on the iPhone and are not syncing with iCloud, then your content is in your iCloud backup. Either way, your calendar is backed up or available.