Determine Whether Two Date Ranges Overlap

(StartA <= EndB) and (EndA >= StartB)

Proof:
Let ConditionA Mean that DateRange A Completely After DateRange B

_                        |---- DateRange A ------|
|---Date Range B -----|                          _

(True if StartA > EndB)

Let ConditionB Mean that DateRange A is Completely Before DateRange B

|---- DateRange A -----|                        _ 
_                          |---Date Range B ----|

(True if EndA < StartB)

Then Overlap exists if Neither A Nor B is true -
(If one range is neither completely after the other,
nor completely before the other, then they must overlap.)

Now one of De Morgan's laws says that:

Not (A Or B) <=> Not A And Not B

Which translates to: (StartA <= EndB) and (EndA >= StartB)

NOTE: This includes conditions where the edges overlap exactly. If you wish to exclude that,
change the >= operators to >, and <= to <

NOTE2. Thanks to @Baodad, see this blog, the actual overlap is least of:
{ endA-startA, endA - startB, endB-startA, endB - startB }

(StartA <= EndB) and (EndA >= StartB) (StartA <= EndB) and (StartB <= EndA)

NOTE3. Thanks to @tomosius, a shorter version reads:
DateRangesOverlap = max(start1, start2) < min(end1, end2)
This is actually a syntactical shortcut for what is a longer implementation, which includes extra checks to verify that the start dates are on or before the endDates. Deriving this from above:

If start and end dates can be out of order, i.e., if it is possible that startA > endA or startB > endB, then you also have to check that they are in order, so that means you have to add two additional validity rules:
(StartA <= EndB) and (StartB <= EndA) and (StartA <= EndA) and (StartB <= EndB) or:
(StartA <= EndB) and (StartA <= EndA) and (StartB <= EndA) and (StartB <= EndB) or,
(StartA <= Min(EndA, EndB) and (StartB <= Min(EndA, EndB)) or:
(Max(StartA, StartB) <= Min(EndA, EndB)

But to implement Min() and Max(), you have to code, (using C ternary for terseness),:
(StartA > StartB? Start A: StartB) <= (EndA < EndB? EndA: EndB)

I believe that it is sufficient to say that the two ranges overlap if:

(StartDate1 <= EndDate2) and (StartDate2 <= EndDate1)

For reasoning about temporal relations (or any other interval relations, come to that), consider Allen's Interval Algebra. It describes the 13 possible relations that two intervals can have with respect to each other. You can find other references — "Allen Interval" seems to be an operative search term. You can also find information about these operations in Snodgrass's Developing Time-Oriented Applications in SQL (PDF available online at URL), and in Date, Darwen and Lorentzos Temporal Data and the Relational Model (2002) or Time and Relational Theory: Temporal Databases in the Relational Model and SQL (2014; effectively the second edition of TD&RM).

The short(ish) answer is: given two date intervals A and B with components .start and .end and the constraint .start <= .end, then two intervals overlap if:

A.end >= B.start AND A.start <= B.end

You can tune the use of >= vs > and <= vs < to meet your requirements for degree of overlap.

ErikE comments:

You can only get 13 if you count things funny... I can get "15 possible relations that two intervals can have" when I go crazy with it. By sensible counting, I get only six, and if you throw out caring whether A or B comes first, I get only three (no intersect, partially intersect, one wholly within other). 15 goes like this: [before:before, start, within, end, after], [start:start, within, end, after], [within:within, end, after], [end:end, after], [after:after].

I think that you cannot count the two entries 'before:before' and 'after:after'. I could see 7 entries if you equate some relations with their inverses (see the diagram in the referenced Wikipedia URL; it has 7 entries, 6 of which have a different inverse, with equals not having a distinct inverse). And whether three is sensible depends on your requirements.

----------------------|-------A-------|----------------------
    |----B1----|
           |----B2----|
               |----B3----|
               |----------B4----------|
               |----------------B5----------------|
                      |----B6----|
----------------------|-------A-------|----------------------
                      |------B7-------|
                      |----------B8-----------|
                         |----B9----|
                         |----B10-----|
                         |--------B11--------|
                                      |----B12----|
                                         |----B13----|
----------------------|-------A-------|----------------------

Here is the code that does the magic:

 var isOverlapping =  ((A == null || D == null || A <= D) 
            && (C == null || B == null || C <= B)
            && (A == null || B == null || A <= B)
            && (C == null || D == null || C <= D));

Where..

• A -> 1Start
• B -> 1End
• C -> 2Start
• D -> 2End

Proof? Check out this test console code gist.

An easy way to remember the solution would be
min(ends)>max(starts)

I would do

StartDate1.IsBetween(StartDate2, EndDate2) || EndDate1.IsBetween(StartDate2, EndDate2)

Where IsBetween is something like

    public static bool IsBetween(this DateTime value, DateTime left, DateTime right) {
        return (value > left && value < right) || (value < left && value > right);
    }

The solution posted here did not work for all overlapping ranges...

----------------------|-------A-------|----------------------
    |----B1----|
           |----B2----|
               |----B3----|
               |----------B4----------|
               |----------------B5----------------|
                      |----B6----|
----------------------|-------A-------|----------------------
                      |------B7-------|
                      |----------B8-----------|
                         |----B9----|
                         |----B10-----|
                         |--------B11--------|
                                      |----B12----|
                                         |----B13----|
----------------------|-------A-------|----------------------

my working solution was:

AND (
  ('start_date' BETWEEN STARTDATE AND ENDDATE) -- caters for inner and end date outer
  OR
  ('end_date' BETWEEN STARTDATE AND ENDDATE) -- caters for inner and start date outer
  OR
  (STARTDATE BETWEEN 'start_date' AND 'end_date') -- only one needed for outer range where dates are inside.
) 

As there have been several answers for different languages and environments, here is one for standard ANSI SQL.

In standard SQL it is as as simple as

(StartDate1, EndDate1) overlaps (StartDate2, EndDate2)

assuming all four columns are DATE or TIMESTAMP columns. It returns true if both ranges have at least one day in common (assuming DATE values)

(However not all DBMS products support that)

In PostgreSQL it's also easy to test for inclusion by using date ranges

daterange(StartDate1, EndDate1) @> daterange(StartDate2, EndDate2)

the above returns true if the second range is completely included in the first (which is different to "overlaps")

Short answer using momentjs:

function isOverlapping(startDate1, endDate1, startDate2, endDate2){ 
    return moment(startDate1).isSameOrBefore(endDate2) && 
    moment(startDate2).isSameOrBefore(endDate1);
}

the answer is based on above answers, but its shortened.

The easiest way to do it in my opinion would be to compare if either EndDate1 is before StartDate2 and EndDate2 is before StartDate1.

That of course if you are considering intervals where StartDate is always before EndDate.

If you provide a date range as input and want to find out if it overlaps with the existing date range in database, the following conditions can successfully meet your demand

Assume you provide a @StartDate and @EndDate from your form input.

conditions are :

If @StartDate is ahead of existingStartDate and behind existingEndDate then we can say @StartDate is in the middle of a existing date range, thus we can conclude it will overlap

@StartDate >=existing.StartDate And @StartDate <= existing.EndDate) 

If @StartDate is behind existingStartDate but @EndDate is ahead of existingStartDate we can say that it will overlap

 (@StartDate <= existing.StartDate And @EndDate >= existing.StartDate)

If @StartDate is behind existingStartDate And @EndDate is ahead of existingEndDate we can conclude that the provided date range devours a existing date range , thus overlaps

 (@StartDate <= existing.StartDate And @EndDate >= existing.EndDate))

If any of the condition stands true, your provided date range overlaps with existing ones in the database.

I found another quite simple approach. If start and end date of daterange1 falls before start date of daterange2 or start and end date of daterange1 falls after end date of daterange2 this means they don't intersect with each other.

public boolean doesIntersect(DateRangeModel daterange1, DateRangeModel  daterange2) {
    return !(
            (daterange1.getStartDate().isBefore(daterange2.getStartDate())
                    && daterange1.getEndDate().isBefore(daterange2.getStartDate())) ||
                    (daterange1.getStartDate().isAfter(daterange2.getStartDate())
                            && daterange1.getEndDate().isAfter(daterange2.getEndDate())));
}

As long as there are simple solutions to this, it might not be efficient to use additional packages just to do the simple stuff. However, if you are already using date-fns already in your project, there is a method called areIntervalsOverlapping which does the same thing.

Syntax:

areIntervalsOverlapping(intervalLeft, intervalRight, [options])

Example:

// For overlapping time intervals:
areIntervalsOverlapping(
  { start: new Date(2014, 0, 10), end: new Date(2014, 0, 20) },
  { start: new Date(2014, 0, 17), end: new Date(2014, 0, 21) }
)
//=> true

Here is a generic method that can be usefull locally.

    // Takes a list and returns all records that have overlapping time ranges.
    public static IEnumerable<T> GetOverlappedTimes<T>(IEnumerable<T> list, Func<T, bool> filter, Func<T,DateTime> start, Func<T, DateTime> end)
    {
        // Selects all records that match filter() on left side and returns all records on right side that overlap.
        var overlap = from t1 in list
                      where filter(t1)
                      from t2 in list
                      where !object.Equals(t1, t2) // Don't match the same record on right side.
                      let in1 = start(t1)
                      let out1 = end(t1)
                      let in2 = start(t2)
                      let out2 = end(t2)
                      where in1 <= out2 && out1 >= in2
                      let totover = GetMins(in1, out1, in2, out2)
                      select t2;

        return overlap;
    }

    public static void TestOverlap()
    {
        var tl1 = new TempTimeEntry() { ID = 1, Name = "Bill", In = "1/1/08 1:00pm".ToDate(), Out = "1/1/08 4:00pm".ToDate() };
        var tl2 = new TempTimeEntry() { ID = 2, Name = "John", In = "1/1/08 5:00pm".ToDate(), Out = "1/1/08 6:00pm".ToDate() };
        var tl3 = new TempTimeEntry() { ID = 3, Name = "Lisa", In = "1/1/08 7:00pm".ToDate(), Out = "1/1/08 9:00pm".ToDate() };
        var tl4 = new TempTimeEntry() { ID = 4, Name = "Joe", In = "1/1/08 3:00pm".ToDate(), Out = "1/1/08 8:00pm".ToDate() };
        var tl5 = new TempTimeEntry() { ID = 1, Name = "Bill", In = "1/1/08 8:01pm".ToDate(), Out = "1/1/08 8:00pm".ToDate() };
        var list = new List<TempTimeEntry>() { tl1, tl2, tl3, tl4, tl5 };
        var overlap = GetOverlappedTimes(list, (TempTimeEntry t1)=>t1.ID==1, (TempTimeEntry tIn) => tIn.In, (TempTimeEntry tOut) => tOut.Out);

        Console.WriteLine("\nRecords overlap:");
        foreach (var tl in overlap)
            Console.WriteLine("Name:{0} T1In:{1} T1Out:{2}", tl.Name, tl.In, tl.Out);
        Console.WriteLine("Done");

        /*  Output:
            Records overlap:
            Name:Joe T1In:1/1/2008 3:00:00 PM T1Out:1/1/2008 8:00:00 PM
            Name:Lisa T1In:1/1/2008 7:00:00 PM T1Out:1/1/2008 9:00:00 PM
            Done
         */
    }

a compact formula that works for me

class ValidityRuleRange {
        private final Date from;
        private final Date to;
    ...
    private boolean isOverlap(ValidityRuleRange vrr) {
        int c1 = from.compareTo(vrr.getTo());
        int c2 = to.compareTo(vrr.getFrom());
        return c1 == 0 || c2 == 0 || c1 + c2 == 0;
    }