sql-update-query-using-joins

You don't quite have SQL Server's proprietary UPDATE FROM syntax down. Also not sure why you needed to join on the CommonField and also filter on it afterward. Try this:

UPDATE t1
  SET t1.CalculatedColumn = t2.[Calculated Column]
  FROM dbo.Table1 AS t1
  INNER JOIN dbo.Table2 AS t2
  ON t1.CommonField = t2.[Common Field]
  WHERE t1.BatchNo = '110';