The backup space estimate (like the estimate that’s made for enough free space to upgrade) can be wrong, and it’s almost always wrong by over estimating the data.
Here’s steps to move forward that are better IMO than previously documented.
- Put the phone in airplane mode ( no WiFi / no cellular) be sure WiFi is off since if you used WiFi before in airplane mode it will still be on.
- Power off the iPhone
- 20 seconds after it’s off, plug into power and once you see it start, let it sit for 10 minutes (to let the space calculation run without any sync causing hiccups). Wait up to 10 more minutes if the space calculation is all gray or other and you don't get realistic information from the storage space calculation.
- Open iPhone storage (settings > general > iPhone Storage) and see how much space is used (screenshot if needed for uploading here or for Apple support later)
- My notes is 7.02 GB my Health is 2.35 GB and my contacts 0.3 GB
- Try to back up only the smallest item (turn off all other backup data) and get a short, good clean backup. (This means turn off airplane mode now)
- Repeat turning on things you want backed up one by one for the next larger item until you agree the space in iCloud is full or you’re done.
Worst case, you will need to contact Apple support if the numbers don’t match up. They can fix things on the server side if the calculation is really off for your account. I’ve also purchased extra storage for one month to let a big backup happen and then cleaned things and slimmed down and cancelled the storage a few weeks later once I had time to clean house on the iPhone.