Do I need to reformat my mac

Most likely you will need to erase the drive, but you can try this:

Repair the Drive for El Capitan or Later

1. Restart the computer and after the chime hold down the Command and R keys until the Utility Menu appears.
2. Select Disk Utility and press the Continue button.
3. Then select the indented (usually, Macintosh HD) volume entry from the side list.
4. Click on the First Aid tab in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
5. Select Restart from the Apple menu.

If the above fails to work:

Install El Capitan or Later from Scratch

Backup if possible before continuing.

1. Restart the computer. Immediately after the chime hold down the CommandandRkeys until the Apple logo appears. When the Utility Menu appears:
2. Select Disk Utility from the Utility Menu and click on Continue button.
3. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the Device list.
4. Click on the Erase icon in Disk Utility's main window. A panel will drop down.
5. Set the Format type to Mac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Select Reinstall OS X and click on the Continue button.

If you don't have a functioning Recovery HD from which to boot:

Clean Install of El Capitan or Later on a Clean Disk

1. Restart the computer. Immediately after the chime hold down the Command-Option-Rkeys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Erase tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Reinstall OS X and click on the Continue button.

This should install the version of OS X that was pre-installed when the computer was new.