How much free space I need on my computer to make a backup?

There is no fixed answer as to how much space would be required, because this is a variable depending on what you choose to backup and how often you backup, also what has changed on your iPhone since your last backup.

If the current status of your iPhone is what you want to backup, then you could move your old backup folder into another storage device like and external drive, or even delete it. (Please note: if you do delete it, you will not be able to revert: restore an iPhone to that previous backed up state.)

After clearing out the old backup from your PC, you can make a fresh (new) backup of your iPhone as it is now. And hopefully, there will be enough space on your PC for it.

This article will hep you manage your backup folder on your PC. I hope it will bring some clarity to your issue. Kindly let us know if you have further queries. Good Luck!

Locate backups of your iPhone, iPad, and iPod touch - Apple Support

Watch the iTunes BackUp Size on a GIF below

Note this is a compressed backup size. (During restoration it will expand)

See the GIF which shows as 28.03 GB used space on iPhone 6 and the Backup Size id 5.26GB

Same is true for iCloud Backup too. What you see the size is compressed Size

iCloud backup size on iCloud is 3.5 GB for the same iPhone same date that is because iCloud backup doesn’t include information that are synced and stored in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, Voice Memos, shared photos, iCloud Photos*, Health data, call history, and files you store in iCloud Drive.

*-If you had turned on iCloud Photos, your content is automatically stored in iCloud. 

Watch the GIF below

What does iCloud back up? - Apple Support