Calculate the time period a certain field is overlapping in SQL Server

I am currently trying to figure out the overlapping time period between records. I already have a query that indicates if it is overlapping another field with ‘yes’ and ‘no’. But I need to have the exact duration of the overlapping time period when the field has ‘yes’ as indication. Can someone help me with it?

Query:

CASE 
    WHEN 
        ([StartDateTime] BETWEEN (LAG([StartDateTime], 1) OVER (ORDER BY [aaID])) 
                             AND (LAG([EndDateTime], 1) OVER (ORDER BY [aaID]))) OR
        ([EndDateTime] BETWEEN (LAG([StartDateTime], 1) OVER (ORDER BY [aaID])) 
                           AND (LAG([EndDateTime], 1) OVER (ORDER BY [aaID]))) OR
        ([StartDateTime] < (LAG([StartDateTime], 1) OVER (ORDER BY [aaID])) 
         AND [EndDateTime] > (LAG([EndDateTime], 1) OVER (ORDER BY [aaID]))) OR
        ([StartDateTime] > (LAG([StartDateTime], 1) OVER (ORDER BY [aaID])) 
         AND [EndDateTime] < (LAG([EndDateTime], 1) OVER (ORDER BY [aaID])))
        THEN 'yes'
    WHEN (LAG([StartDateTime], 1) OVER (ORDER BY [aaID])) IS NULL
        THEN NULL
    ELSE 'no'
END AS [OverLapping with Previous]

Result:

Answer

Check this for the difference in days.

case when ([StartDateTime] >= (lag([StartDateTime],1) over (order by [aaIDID])) and [EndDateTime] <= (lag([EndDateTime],1) over (order by [aaIDID]))) 
     Then DateDiff(day, [StartDateTime], [EndDateTime])
     when ([StartDateTime] <= (lag([StartDateTime],1) over (order by [aaIDID])) and [EndDateTime] >= (lag([EndDateTime],1) over (order by [aaIDID])))
     Then DateDiff(day, (lag([StartDateTime],1) over (order by [aaIDID])), (lag([EndDateTime],1) over (order by [aaIDID])))
     when ([StartDateTime] < (lag([StartDateTime],1) over (order by [aaIDID])) and [EndDateTime] < (lag([EndDateTime],1) over (order by [aaIDID]))) And [EndDateTime] > (lag([StartDateTime],1) over (order by [aaIDID]))
     Then DateDiff(day, (lag([StartDateTime],1) over (order by [aaIDID])), [EndDateTime])
     when ([StartDateTime] > (lag([StartDateTime],1) over (order by [aaIDID])) and [EndDateTime] > (lag([EndDateTime],1) over (order by [aaIDID]))) And [StartDateTime] < (lag([EndDateTime],1) over (order by [aaIDID]))
     Then DateDiff(day, [StartDateTime], (lag([EndDateTime],1) over (order by [aaIDID])))
end as Diff