Hm complex question as Apple confuse the issue with both names and numbers. Here is a list of what compatibility there is. Note that you may have to delve a little deeper if you have and 3rd party software to gain compatibility knowledge.
Big Sur compatibility
Big Sur is the next version of macOS. It's currently in beta, but it will be available to install on Macs later in 2020. Here's a list of the Macs that will be able to run macOS Big Sur:
- MacBook models from early 2015 or later
- MacBook Air models from 2013 or later
- MacBook Pro models from 2013 or later
- Mac mini models from 2014 or later
- iMac models from 2014 or later
- iMac Pro (all models)
- Mac Pro models from 2013 or later
Catalina compatibility
Catalina arrived in October 2019 and supports the following Macs:
- MacBook (Early 2015 or later)
- MacBook Air (Mid-2012 or later)
- MacBook Pro (Mid-2012 or later)
- Mac mini (Late 2012 or later)
- iMac models late 2012 or later
- iMac Pro (all models)
- Mac Pro (late 2013)
Mojave compatibility
Mojave arrived in September 2018 and supported the following Macs:
- MacBook (Early 2015 or newer)
- MacBook Air (Mid 2012 or newer)
- MacBook Pro (Mid 2012 or newer)
- Mac mini (Late 2012 or newer)
- iMac (Late 2012 or newer)
- iMac Pro (all models)
- Mac Pro (Late 2013, plus mid-2010 and mid-2012 models with recommended Metal-capable GPU)
High Sierra compatibility
High Sierra arrived in September 2017 and supported the following Macs:
- MacBook (Late 2009 or newer)
- MacBook Pro (Mid 2010 or newer)
- MacBook Air (Late 2010 or newer)
- Mac mini (Mid 2010 or newer)
- iMac (Late 2009 or newer)
- Mac Pro (Mid 2010 or newer)
Sierra compatibility
Sierra arrived in September 2016 and supported the following Macs:
- MacBook (Late 2009 or newer)
- MacBook Pro (Mid 2010 or newer)
- MacBook Air (Late 2010 or newer)
- Mac mini (Mid 2010 or newer)
- iMac (Late 2009 or newer)
- Mac Pro (Mid 2010 or newer)
El Capitan compatibility
El Capitan arrived in September 2015 and supported the following Macs:
- MacBook (Early 2015)
- MacBook (Late 2008 Aluminium, or Early 2009 or newer)
- MacBook Pro (Mid/Late 2007 or newer)
- MacBook Air (Late 2008 or newer)
- Mac mini (Early 2009 or newer)
- iMac (Mid 2007 or newer)
- Mac Pro (Early 2008 or newer)
- Xserve (Early 2009)
Yosemite compatibility
Yosemite arrived in October 2014 and supported the following Macs:
- iMac (Mid-2007 or later)
- MacBook (13" Late 2008 Aluminum, Early 2009 or later)
- MacBook Pro (13" Mid-2009 or later)
- MacBook Pro (15" Mid/Late 2007 or later)
- MacBook Pro (17" Late 2007 or later)
- MacBook Air (Late 2008 or later)
- Mac mini (Early 2009 or later)
- Mac Pro (Early 2008 or later)
- Xserve (Early 2009)
Mavericks compatibility
Mavericks arrived in October 2013 and supported the following Macs:
- iMac (Mid 2007 or newer)
- MacBook (Late 2008 Aluminum, or Early 2009 or newer)
- MacBook Pro (Mid/Late 2007 or newer)
- Xserve (Early 2009)
- MacBook Air (Late 2008 or newer)
- Mac mini (Early 2009 or newer)
- Mac Pro (Early 2008 or newer)
Mountain Lion compatibility
Mountain Lion, the last of the 'cat' versions of macOS launched in July 2012 and supported the following Macs:
- iMac (Mid-2007 or newer)
- MacBook (Late 2008 Aluminum, or Early 2009 or newer)
- MacBook Air (Late 2008 or newer)
- MacBook Pro (Mid/Late 2007 or newer)
- Mac mini (Early 2009 or newer)
- Mac Pro (Early 2008 or newer)
- Xserve (Early 2009)
And this table puts the numbers to versions:-
available):
OS X 10 beta: Kodiak - 13 September 2000
OS X 10.0: Cheetah - 24 March 2001
OS X 10.1: Puma - 25 September 2001
OS X 10.2: Jaguar - 24 August 2002
OS X 10.3 Panther (Pinot) - 24 October 2003
OS X 10.4 Tiger (Merlot) - 29 April 2005
[OS X 10.4.4 Tiger (Chardonnay)]
OS X 10.5 Leopard (Chablis) - 26 October 2007
OS X 10.6 Snow Leopard - 28 August 2009
OS X 10.7 Lion (Barolo) - 20 July 2011
OS X 10.8 Mountain Lion (Zinfandel) - 25 July 2012
OS X 10.9 Mavericks (Cabernet) - 22 October 2013
OS X 10.10: Yosemite (Syrah) - 16 October 2014
OS X 10.11: El Capitan (Gala) - 30 September 2015
macOS 10.12: Sierra (Fuji) - 20 September 2016
macOS 10.13: High Sierra (Lobo) - 25 September 2017
macOS 10.14: Mojave (Liberty) - 24 September 2018
macOS 10.15: Catalina (Jazz) - 7 October 2019
macOS 11: Big Sur - currently in betaMacs:
Interesting that at last when Big Sur emerges they will be moving on from version 10! Though Big Sur will have some backwards compatibility it does not go back much more than the list below as shown further above.
- Typically my big iMac is dated around 2012, so I am stuck at Mojave.