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sql - ADD time 23:59:59.999 to end date for between

I have been having an issue with using the following:

Column_Name BETWEEN @StartDate AND @EndDate. 

This is because the @EndDate = 00:00:00.000 for the time, which doesn't pick up all the values for that day.

How would I convert the @EndDate (Always 00:00:00.000) to always be Date + 23:59:59.999?

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One option that avoids needing to add EndDate + 23:59:59.999 is to not use the between comparison and instead use column_name >= @StartDate and column_name < @EndDate +1


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