Date Intervals

This page describes a few methods for working with intervals of dates.   Specifically, it address the questions of whether a date falls within an interval, the number of days that two intervals overlap, and the how many days are in one interval, excluding those days in another interval.  These formulas can be quite useful for scheduling applications, such as employee vacation schedules.

Is A Date In An Interval?

Suppose we have 3 dates -- a start date, and end date, and a test date.   We can test whether the test date falls within the interval between start date and end date.   In this formula, we will use three named cells:  TDate1 for the start date, TDate2 for the end date, and TDate for the test date.  This formula will return either TRUE or  FALSE, indicating whether TDate falls in the interval.

=AND((TDate>=MIN(TDate1,TDate2)),TDate<=MAX(TDate1,TDate2))

For example if  TDate1 is 1-Jan and TDate2 is 31-Jan , and TDate is 15-Jan , the formula will return TRUE, indicating that  TDate falls in the interval.

In this formula, it does not matter whether TDate1 is earlier or later than TDate2

Number Of Days In One Interval And Not In Another

We can also work with two date intervals, and determine the number of days that fall in one interval, and not in another.  This can become complicated because of how the intervals may overlap.  For example, the main interval may complete contain the exclusion interval.  Or, the exclusion interval may completely contain the main interval.  Moreover, only part of the main interval may be contained within the exclusion interval, either at the starting or the ending end of the interval.  Finally, the two intervals may not overlap at all.

Below is a summary of the various interval types.  The Dates values are the days we wish to count.  The VDates values are the days we wish to exclude from the Dates interval.   The complexity of the formula is due to the fact that it must handle all of the interval types. For this formula, we will have 4 named cells, as shown below:

 Name Description Date1 The starting date of the main interval.  The main interval is the dates we want to work count. Date2 The ending date of the main interval. VDate1 The starting date of the exclusion interval.  The exclusion interval is the dates that we want to exclude from the count of the main interval. VDate2 The ending date of the exclusion interval. NWRange A list of holiday dates.  Used in the second version of the formula, which uses the NETWORKDAYS function.

For this formula, we require that Date1 is less than (earlier than) or equal to Date2, and that VDate1 is less than (earlier than) or equal to VDate2.

=IF(OR(Date2<VDate1,VDate2<Date1),Date2-Date1+1,IF(OR(AND(Date1<=VDate1,Date2>=VDate2),
AND(Date1>=VDate1,Date2<=VDate2)),MAX(0,(Date2-Date1)-(VDate2-VDate1)),
IF(OR(AND(Date1<=VDate1,Date2<=VDate2),AND(Date1>=VDate1,Date2>VDate2)),
MAX(0,(VDate1-Date1))+MAX(0,Date2-VDate2),NA())))

Here are some examples.

 Date1 Date2 VDate1 VDate2 Result Description 1-Jan 31-Jan 10-Jan 20-Jan 20 There are 20 days between 1-Jan and 9-Jan (9 days) and 21-Jan and 31-Jan (11 days).  The 11 days between 10-Jan and 20-Jan are subtracted from the 31 days between 1-Jan and 31-Jan.  In this example, the entire exclusion interval (the VDates) is included within the main interval (the Dates). 10-Jan 20-Jan 1-Jan 31-Jan 0 Here, the entire main interval is included within the exclusion interval.  There are no days between 10-Jan and 20-Jan that do fall outside the 1-Jan and 31-Jan. 1-Jan 15-Jan 10-Jan 20-Jan 9 In this case, the ending segment of the main interval (1-Jan to 15-Jan) overlaps with the beginning segment of the exclusion interval (10-Jan to 20-Jan).  There are 9 days (1-Jan to 9-Jan) in the main interval that do not overlap with the exclusion interval. 10-Jan 20-Jan 1-Jan 15-Jan 5 Ending segment of the main interval overlaps the exclusion interval.  There are 5 days (16-Jan to 20-Jan) in the main interval that are not included in the exclusion segement.

Note that the dates here are inclusive.  There are 10 days between 1-Jan and 10-Jan.  This is one day different that what you would get from simply subtracting the dates.

The formula above does not treat weekend days differently from working days.   In other words, Saturdays and Sundays are included in the calculations.  If you want to count only weekdays, excluding weekends and holidays, use the modified version below, which calls the NETWORKDAYS function to compute the number of working days in the intervals.  This function adds another name ranged to the mix.  This name, NWRange, refers to a range containing a list of holidays.  If you do not use holidays, you can either point this name to an empty cell, or eliminate it from the formula entirely.

=IF(OR(Date2<VDate1,VDate2<Date1),NETWORKDAYS(Date1,Date2,NWRange),
IF(OR(AND(Date1<=VDate1,Date2>=VDate2),AND(Date1>=VDate1,Date2<=VDate2)),
MAX(0,NETWORKDAYS(Date1,Date2,NWRange)-NETWORKDAYS(VDate1,VDate2,NWRange)),
IF(OR(AND(Date1<=VDate1,Date2<=VDate2),AND(Date1>=VDate1,Date2>VDate2)),
IF((Date1>=VDate1),0,NETWORKDAYS(Date1,VDate1-1,NWRange))+
IF((Date2<=VDate2),0,NETWORKDAYS(VDate2+1,Date2,NWRange)),NA())))

The NETWORKDAYS function is part of the Analysis Tool Pack Add-In, so you must have this module installed in order to use this formula.  For more information about using formulas to create the dates of holidays, see the Holidays page.

Tangent:
The reason the named cells are
VDate1 and VDate2 is that I originally wrote this formula for a Vacation timekeeping application, and the V refers to "Vacation".   Of course, you can name your cells anything that works with your application, or you can simply use cell references.

Number Of Days Common To Two Intervals

The  previous section worked with a logical NOT condition -- dates in one interval and NOT in another.  This section describes a formula for working with the inverse of that -- the number of days that are in BOTH of two intervals.

For this formula, we will have 4 named cells, as shown below:

 Name Description IDate1 The starting date of the first interval. IDate2 The ending date of the first interval. RDate1 The starting date of the second interval. RDate2 The ending date of the second interval. NWRange A list of holiday dates.  Used in the second version of the formula, which uses the NETWORKDAYS function.

For this formula, we require that IDate1 is less than (earlier than) or equal to IDate2, and that RDate1 is less than (earlier than) or equal to RDate2. The formula below will return the number of days that are in both intervals.

=IF(OR(IDate2<RDate1,IDate1>RDate2),0,(MIN(IDate2,RDate2)-MAX(IDate1,RDate1)+1))

Here are some examples.

 IDate1 IDate2 RDate1 RDate2 Result Description 1-Jan 31-Jan 10-Jan 20-Jan 11 There are 11 days common to the intervals.   Since the RDates are contained within the IDates, the result is the number of days between 10-Jan and 20-Jan, or 11 days. 10-Jan 20-Jan 1-Jan 31-Jan 11 Since this is an AND condition format, we can reverse the dates between IDates and RDates, and get the same result as above, 11 days. 1-Jan 15-Jan 10-Jan 20-Jan 6 Here, there are 6 days common to the two intervals -- the dates 10-Jan to 15-Jan fall in both intervals. 1-Jan 10-Jan 15-Jan 20-Jan 0 The result here is 0, because there are no dates in the IDate interval (1-Jan to 10-Jan) than fall in the RDate interval (15-Jan to 20-Jan).

Note that the dates here are inclusive.  There are 10 days between 1-Jan and 10-Jan.  This is one day different that what you would get from simply subtracting the dates.

The formula above does not treat weekend days differently from working days.   In other words, Saturdays and Sundays are included in the calculations.  If you want to count only weekdays, excluding weekends and holidays, use the modified version below, which calls the NETWORKDAYS function to compute the number of working days in the intervals.  This function adds another name ranged to the mix.  This name, NWRange, refers to a range containing a list of holidays.  If you do not use holidays, you can either point this name to an empty cell, or eliminate it from the formula entirely.

=IF(OR(IDate2<RDate1,IDate1>RDate2),0,
ABS(NETWORKDAYS(MIN(IDate2,RDate2),MAX(IDate1,RDate1),NWRange)))

The
NETWORKDAYS function is part of the Analysis Tool Pack Add-In, so you must have this module installed in order to use this formula.  For more information about using formulas to create the dates of holidays, see the Holidays page.

A final note:   These formulas are designed to illustrate the concept of the date "intervals", and how they need to be handled by the Excel date arithmetic.  Logicians can probably reduce the formulas to simpler forms by consolidating the ANDs and ORs.  But the point here is illustration and education, not the simplest possible formula.
 Other Date And Time Related Procedures are described on the following pages. Adding Months And Years The DATEDIF Function Date Intervals Dates And Times Date And Time Entry Date And Time Arithmetic Distributing Dates Over Intervals Holidays Julian Dates Latitude And Longitude  Overtime Hours And Timesheets VBA Procedures For Dates And Times Week Numbers Worksheet Functions For Dates And Times See the Dates And Times Topic Index For Information