Cd's and dvd's do not get formatted or reformatted. Since new laptops and desktops don't have optical drives any more it's best not to use them. Use external media like ext. hard drives, thumb drives, cloud storage etc. Those are safer and more permanent. Optical drives can usually be ordered on desktops for a fee.

Rewritable cds never did work well and have a high failure rate. Don't use for any important files like backups. Win 10 cd player programs might not even recognize them.

https://simple.wikipedia.org/wiki/CD-RW

https://www.dummies.com/computers/operating-systems/windows-10/how-to-copy-files-to-a-cd-or-dvd-in-windows-10/ 

Yes. Formatting a CD allows you to write files on-the-fly (packet writing) instead of compiling the layout first and then burning them to the disc. There is no format option on the right-click context menu for the CD drive, but you should be getting a message asking what type of filesystem that you want to use when you double-click on the drive icon with a blank disc inserted.

I agree with @Mary G. Use something else for saving files. Writable CD's/DVD's were designed for archiving and were never really meant to be used as an everyday medium. That was kind of a gimmick.

However, the reply did not answer the question.  I have the same problem and I lost the ability to format a CD-RW.  I need this capability (forget about what is better than CD-RW).  How can I get the right click / format option back?

You may want to take a look at this thread...

DW316, used to format DVD but still read and burns to previous disks

Dell company is VERY VERY VERY VERY VERY VERY VERY VERY SUPERMASSIVE UNHELPFUL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

WHY NO FORMAT OPTION ON THE INTERNAL DVD DRIVE ON MY DESKTOP COMPUTER? I had to reinstall the system TWO TIMES and finally had a format option for about 1-2 weeks and then disappeared again and FAILED!!!!!!!!!!!!!!

I had this issue nearly a year ago and found a suggestion on a Microsoft Communities Thread forum similar to this that corrected the problem for me.  All you have to do is open the Windows Registry Editor and delete the NoCDBurningDWORD key from two locations:

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Policies\Explorer

HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Policies\Explorer

Restart your computer and you should be able to format a blank CD or DVD again.  Periodically when I receive a Windows Update, I will have to perform the procedure outlined above.

How to open the Register in Windows 10:

1. In the search box on the taskbar

How to open the Register in Windows 10:
1. In the search box on the taskbar, type regedit. Then select the top result for Register Editor.
2. Press and hold or right-click the Start button, then select Run. Enter regedit in the open box and select OK.
I take no credit for this fix, I am just repeating what I found to work for me.

Thank you!