Maximum Connections for SQL Server

All About Connections

@@MAX_Connections Returns the maximum number of simultaneous user connections allowed on an instance of SQL Server. The number returned is not necessarily the number currently configured

Select @@MAX_Connections as Max_Connections

No of attempted connections for SQL Server

Select @@Connections as TotalLoginAttempts

This will include either successful or unsuccessful since SQL Server was last started.

You can also check the same using sp_monitor System procedure

Exec sp_monitor