How to update my iPhone 13 to iOS 16.1?

Connect to WiFi and go to Settings > General > Software Update.

1. Turn off any VPN you are using.
2. Make sure you have 10GB of free space.
3. Turn off Low Power mode.
4. Have a 50% battery charge or more and preferably connect it to power.
5. If you have a beta profile remove it.

Yes, your battery will probably no longer show 100% because your battery does not have 100% health assuming that you have actually been using this iPhone. Batteries are a consumable, the health goes down as you use the iPhone. It may show around 91% after you update. Because it probably is at 91% health.

Yes. Use a computer or the Software Update function in Settings; if you encounter a specific issue, describe it in this thread.

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You are still at 100% battery health after 8 months? That is rather amazing and probably inaccurate. This will change with an update to be more accurate.

Yes, never doubted you. One of the later updates addressed the battery health calculation. You must have automatic updates turned off.

Yes they will be I hope you are regularly backing up your iPhone either to your computer or iCloud. Do a backup just before updating.