@Bretana给出的数学解很好，但忽略了两个具体细节：

封闭或半开放间隔的方面空间隔

关于区间边界的封闭或开放状态，@Bretana的解对封闭区间有效

（起点A<=终点B）和（终点A>=起点B）

可以重写为半开间隔：

（开始A<结束B）和（结束A>开始B）

这种校正是必要的，因为根据定义，开放区间边界不属于区间的值范围。

关于空间隔，这里上面所示的关系不成立。根据定义不包含任何有效值的空间隔必须作为特殊情况处理。我通过Java时间库Time4J通过以下示例进行了演示：

MomentInterval a = MomentInterval.between(Instant.now(), Instant.now().plusSeconds(2));
MomentInterval b = a.collapse(); // make b an empty interval out of a

System.out.println(a); // [2017-04-10T05:28:11,909000000Z/2017-04-10T05:28:13,909000000Z)
System.out.println(b); // [2017-04-10T05:28:11,909000000Z/2017-04-10T05:28:11,909000000Z)

前导方括号“[”表示封闭的开始，而最后一个括号“）”表示开放的结束。

System.out.println(
      "startA < endB: " + a.getStartAsInstant().isBefore(b.getEndAsInstant())); // false
System.out.println(
      "endA > startB: " + a.getEndAsInstant().isAfter(b.getStartAsInstant())); // true

System.out.println("a overlaps b: " + a.intersects(b)); // a overlaps b: false

如上所示，空间隔违反了上面的重叠条件（尤其是startA<endB），因此Time4J（以及其他库）必须将其作为特殊的边缘情况来处理，以确保任何任意间隔与空间隔的重叠都不存在。当然，日期间隔（默认情况下在Time4J中是关闭的，但也可以是半开的，就像空日期间隔一样）的处理方式类似。

我认为最简单的方法是比较EndDate1是否在StartDate2之前，EndDate2是否在StartDate 1之前。

当然，如果您正在考虑StartDate总是在EndDate之前的时间间隔。

如果重叠本身也需要计算，可以使用以下公式：

overlap = max(0, min(EndDate1, EndDate2) - max(StartDate1, StartDate2))
if (overlap > 0) { 
    ...
}

在Microsoft SQL SERVER中-SQL函数

CREATE FUNCTION IsOverlapDates 
(
    @startDate1 as datetime,
    @endDate1 as datetime,
    @startDate2 as datetime,
    @endDate2 as datetime
)
RETURNS int
AS
BEGIN
DECLARE @Overlap as int
SET @Overlap = (SELECT CASE WHEN  (
        (@startDate1 BETWEEN @startDate2 AND @endDate2) -- caters for inner and end date outer
        OR
        (@endDate1 BETWEEN @startDate2 AND @endDate2) -- caters for inner and start date outer
        OR
        (@startDate2 BETWEEN @startDate1 AND @endDate1) -- only one needed for outer range where dates are inside.
        ) THEN 1 ELSE 0 END
    )
    RETURN @Overlap

END
GO

--Execution of the above code
DECLARE @startDate1 as datetime
DECLARE @endDate1 as datetime
DECLARE @startDate2 as datetime
DECLARE @endDate2 as datetime
DECLARE @Overlap as int
SET @startDate1 = '2014-06-01 01:00:00' 
SET @endDate1 =   '2014-06-01 02:00:00'
SET @startDate2 = '2014-06-01 01:00:00' 
SET @endDate2 =   '2014-06-01 01:30:00'

SET @Overlap = [dbo].[IsOverlapDates]  (@startDate1, @endDate1, @startDate2, @endDate2)

SELECT Overlap = @Overlap

对于ruby，我也发现了这一点：

class Interval < ActiveRecord::Base

  validates_presence_of :start_date, :end_date

  # Check if a given interval overlaps this interval    
  def overlaps?(other)
    (start_date - other.end_date) * (other.start_date - end_date) >= 0
  end

  # Return a scope for all interval overlapping the given interval, including the given interval itself
  named_scope :overlapping, lambda { |interval| {
    :conditions => ["id <> ? AND (DATEDIFF(start_date, ?) * DATEDIFF(?, end_date)) >= 0", interval.id, interval.end_date, interval.start_date]
  }}

end

在这里找到它，解释很好->http://makandracards.com/makandra/984-test-if-two-date-ranges-overlap-in-ruby-or-rails

记住解决方案的一个简单方法是最小（结束）>最大（开始）