Most SharePoint admins waste time hunting for the Central Administration site. They log into multiple servers. They dig through IIS manager hoping to spot it. It is a massive waste of time. You do not need to click around to map your infrastructure. You just need to ask the server directly.
Here is the exact process to locate your CA URL without the guesswork.
The N-Tier Farm Search
If you are running a multi-server architecture, you need to know exactly where your admin center lives. The fastest method is querying your web applications.
Run this PowerShell cmdlet to pull the URL across the farm:
Get-SPWebApplication -IncludeCentralAdministration | Where {$_.DisplayName -match "SharePoint Central Administration*"} | Select DisplayName,Url
That works perfectly when you just need the address. But what if you are troubleshooting a specific node? You need to verify if the machine you are currently logged into is actually the host. The previous command will not confirm that for you.
To verify the local machine, filter by the administration property instead:
Get-SPWebApplication -IncludeCentralAdministration | Where {$_.IsAdministrationWebApplication} | Select DisplayName,Url
The Registry Route
Sometimes you are on a server and the SharePoint PowerShell snap-in is not loaded. Do not panic. You do not need the snap-in to find the truth. The URL is hardcoded into the Windows Registry. You just need to read the right version path.
For SharePoint 2013, query the 15.0 hive:
Get-ItemProperty -Path "HKLM:\SOFTWARE\Microsoft\Shared Tools\Web Server Extensions\15.0\WSS\" -Name CentralAdministrationURL
For SharePoint 2010, simply drop down to the 14.0 path:
Get-ItemProperty -Path "HKLM:\SOFTWARE\Microsoft\Shared Tools\Web Server Extensions\14.0\WSS\" -Name CentralAdministrationURL
Stop guessing where your admin center lives. Do the boring work. Run the commands. Get your answers and move on.