Calculate if time period is contained within a start and end time

Question

I have a problem where I am trying to calculate in Excel if any part of a provided work duty time period is contained within a user defined period which specifies the night working hours e.g. 2330-0559 or 0000-0630.

If I provide a work duty time I want and any part of the duty is within the specified period it needs to be identified. E.g. 2230-0630 duty time is within both examples above.

I can tried a few different solutions and still not got the right way solve it. Maybe someone can help. I also know that 24:00 in excel is used for midnight at the end of the day and 00:00 is used for midnight starting the day as excel works from 0-1 as part of the day.

=OR(MOD(A5,1)>$E$2,MOD(A5,1)<$F$2)

Answer 1

I would work with the number of minutes as decimal and with it make a valid range from "Duty start time" and "Duty end time".

Check if you can make any sense out of this:

Here the example:

https://drive.google.com/file/d/1O1B76srlY8sYQHsV_TiZVzi-7B_18eSj/view?usp=sharing

Update: Sorry for the lack of explanation. Here I try my best to clarify how I did it.

Conversion

First of all I try to convert any time into minutes, so 00:00 is 0 minutes, 01:00 is 60 minutes, 24:00 (excel shows 00:00) is 1440 minutes, 25:00 (excel shows 01:00) is 1500 minutes.

That conversion I do with CONVERT(E2,"day", "mn"), which does convert from day to minutes.

Range Normalization and inclusion

Now every range has to be normalized, that means the "End" has to be always bigger than "Start". For 00:00 to 06:00 this works fine, but for 22:00 to 06:00 it needs to be tweaked. So if "Start" is bigger than "End" then I add 1440 mins (24 hours) to "End". That I do with IF(A6>B6, 1440,0).

You then need to see if any "Duty range" contains the "Night range". That normally is done with the formula if (DutyEnd > NightStart AND DuttyStart < NightEnd) then TRUE.

Challenge 1

That was the main concept. But then if you try to compare a range like 00:00-06:00 contained in 24:00-06-00 it does not work. And that is because the converted minutes are 0-360 and 1440-1830, they don't contain each other.

In E3 to fix this I cut down 1440 with modulo (MOD()), then MOD(1440, 1440) = 0. So even if you use values like 25:00 or 52:00, they will be cut down to the smallest amount of minutes. E.g. 25:00 (1500 mins) = 1:00 = 60 mins, 52:00 (3120 mins) = 4:00 = 240 mins

Challenge 2

We have yet another challenge, the possible comparisons are as follows:

• 00:00-06:00 contained in 00:00-06:00 which in minutes is 0-390 contained in 0-390
• 00:00-06:00 contained in 22:00-06:00 which in minutes is 0-390 contained in 1320-1830
• 22:00-06:00 contained in 00:00-06:00 which in minutes is 1320-1830 contained in 0-390

These last two will not match. So that is why in the "Contains" column (E.g.: E6) I compare against the "Night criteria" - 1400 and + 1400.

Hope it is a bit clear. Let me know otherwise..

Answer 2

UNDERSTANDING DATE AND TIME IN EXCEL

Dates in excel are stored as INTEGERS. They represent the days since 1900/01/1 with that date being 1.

Time is stored as a decimal which represents a fraction of a day. 24 hours is 1, 0.5 is 12 noon. etc.

In other words, everything to the left of the decimal is date and everything to the right is time.

JUST USING TIME AND CROSSING MIDNIGHT

This is problematic from the view point that early morning times are less than the late times of the previous day. The fact of the matter is that they are larger. In our heads we do the mental math of knowing the are the following day but we ignore the date aspect.

A quick way to rectify this is to add the date to your time. Life will become much easier with the math. You may however not want to add full dates to start and end times. WITH THE ASSUMPTION that start and end times are not more than 24 hours the simple work around is is to add 1 to the end time when the end time is less than the start time. This means its the next day.

It the example date you provided, column C was insert to CORRECT the end time. It did the check of end less than start if so add one using the following formula:

=B6+(B6<=A6)

The part in brackets is a logic check. It either evaluates to TRUE or FALSE. When excel runs a boolean (TRUE or FALSE) through a math operator (not a function like sum) it will convert TRUE to 1 and FALSE to 0.

LENGTH

Straight forward math of C minus A since C is always after you start and is the larger of the two numbers.

=C6-A6

CROSSING MIDNIGHT

Need to be a little careful in your definition of crossing midnight when a start time or end time is exactly midnight. Technically speaking you did not cross it if you start or stop on it. The difference is really < versus <= or > versus >=. I will leave that to you to sort out. For the math I used:

=AND(A6<1,C6>=1)

Though I did not use this column for anything else

START CHECK

=OR(A6>$F$2,A6<$G$2)

END CHECK

=OR(B6>$F$2,B6<$G$2)

ANY TIME CHECK

I broke this into three columns. It can be combined into one but wanted to show the working parts. The first check is to see if the start time is before the night start and that the shift end time was after the night start time. The second check was similar for the the fisrt except you want to know if the start time is before the night end time and the shift end time is after the night end time. For the OR case you want to check to see if ANY of columns F through I are true:

COLUMN H
=AND(A6<=$F$2,C6>$F$2)

COLUMN I
=AND(A6<$G$2+1,C6>$G$2+1)

Note the +1 for night end time. This is to reflect that the end time is actually on the following day.

COLUMN J
=OR(F6,G6,H6,I6)
or
=(F6+G6+H6+I6)>=1

Place the above formulas in row 6 and copy down as needed

Answer 3

Well, I think I'm missing something but let's see if this works for you. To make this work:

1. All hours must be typed in hh:mm format
2. Night Criteria End must be on a different day. This means it must be over 00:00 or formulas won't work. If you type something like start criteria=22:00 and night criteria= 23:50, both times would be in the same day, so formulas won't work
3. This formulas only work in periods less than 24 hours. If anytime the different between criterias is over 24 hours, formulas won't work properly.

Now, I replied your data like this:

The trick here is dealing with times without dates. Dates in Excel are înteger numbers and decimal parts are the hours/minutes/seconds. So to compare properly hours like this, you need to add an integer part.

Let me explain. In Excel, 18:00 would be 0,75. And 06:00 would be 0,25. If you try to get the difference between both times, you will get -0,5. In decimal it makes sense, but when trying to convert to time, it makes no sense for Excel. So, as I said before, the trick here is adding integers (in this case, because 06:00 is lower than 18:00, we would add +1), so Excel would make 1,25 - 0,75 = 0,5. And Excel can convert 0,5 to hours, and it will return exactly 12 hours, the right result.

So knowing this, the trick in formulas for your data is comparing ends with starts and add 1 or 2 to compare then properly with your criteria. That way Excel can figure out if a time is later or sooner than a criteria.

All my formulas are these ones:

1. LENGHT: =IF(B5<A5;B5+1-A5;B5-A5)
2. CROSS MIDNIGHT: =IF(Y(B5<A5;B5<>0);TRUE;FALSE)
3. START BETWEEN CRITERIA: =IF(AND(IF(A5<$E$2;A5+2;1+A5)>=1+$E$2;IF(A5<$E$2;A5+2;1+A5)<=$F$2+2);TRUE;FALSE)
4. END BETWEEN CRITERIA: =IF(AND(IF(B5<$E$2;B5+2;1+B5)>=1+$E$2;SI(B5<$E$2;B5+2;1+B5)<=$F$2+2);TRUE;FALSE)
5. ANY PART:=IF(OR(E5=TRUE;F5=TRUE;AND(A5<$E$2;A5+C5>1+$F$2));TRUE;FALSE)

Anyways, I uploaded a file to my Gdrive, in case it may be helpful to download and check the formulas.

This is the best I got. Probably there is a better way, but I hope this can help you, or at least, you can adapt it to your needs.

https://drive.google.com/open?id=1nrZKfyUhED_y6iiPRSUwRf7GhJlBYt-O