Updating iMac 10.13.6 High Sierra

What is the model year of your iMac? The model year of an iMac is available at Apple menu > About This Mac.

A late 2009 through mid 2011 iMac can be upgraded to High Sierra 10.13.6 but no later version. 

A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. 

A mid 2014 and late 2014 iMac can be upgraded to the latest version of Big Sur macOS 11 but no later. 

A late 2015 or mid 2015 iMac can be upgraded to the latest version of Monterey macOS 12 but no later. 

A 2017 iMac can be upgraded to the latest version of Ventura macOS 13 but no later. 

For all of the above, see instructions in: How to download and install macOS - Apple Support

A 2019 or later iMac can be upgraded to the current version of Sonoma macOS 14. See: How to upgrade to macOS Sonoma - Apple Support

Also be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.stclairsoft.com/Go64/

or

 https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

Hi Georgette, you’d need to own an iMac late-2012 to be able to upgrade to the next version of macOS, macOS Mojave. You can check the year of your iMac in  > About This Mac. If your Mac is older, you’d need to acquire a more recent model to be able to use recent versions of macOS.