start up disk is full on macbook air

Disk Space - Free Up

Disk Space – Free Up (2)

Disk Space – Free Up (3)

Disk Space - Free Up - Mavericks

Disk Space Filling Up – OmniDiskSweeper 10.8+

Disk Space Filling Up - WhatSize

It is advisable to keep between 10-15Gbs of storage on your HD, so that your mac can function, if you pack it full then it will only end in failure, so it is prudent to keep moving stuff onto an external drive. Movies and images often take up most space, so only keep the ones on your HD that you think you might need on a daily basis.

Having your mac make local backups is a good idea but when you get home you need to move them to your external drive, after all the point of having backups is incase your HD fails you can restore e your info, but if the backups are on the drive that has failed then you lose all your data.

Quite often the details of storage on your mac is wrong, you can re-index Spotlight to see if it makes a difference,

How to rebuild the Spotlight index on your Mac - Apple Support

The post is in the Sierra forum, Erase Free Space is no longer an option in Disk Utility.

See this article OS X: About Disk Utility's erase free space feature - Apple Support

If you are erasing the free space of your Mac OS X startup volume, you may see this message:

"Your startup disk is almost full.
You need to make more space available on your startup disk by deleting files."

This is a normal, temporary part of the erase free space process. Once the free space has been erased, the disk space is available again.