Convert Local to Synchronized Calendar
- Go to device Settings
- Go to Calendar (or Mail, Contacts, Calendars in iOS9 and below)
- At the bottom select Default Calendar and pick the iCloud account of your choosing.
In app Settings (gear button) > Calendars select only the local calendar you want to convert
If you've more than one convert them one by one unless you want them to be merged into a single calendar.
- Press Settings > Share & Print
- Select Export
- Select Date Range to Export (this is limited by iOS to 1 year max)
- Select Type and mark ICS File
- Press Export
- Select Send by E-mail and mail file to an e-mail account available on your PC or Mac so you'll have a backup
Open the email you just sent and click on ics file. You'll get a question in which calendar you would like to import these events.
After you verified all events are synchronized correctly you now may want to delete your local calendar.
See Add & Delete Local Calendar for instructions.