## Count overlapping days in multiple date ranges, part 2

In the previous post I explained how to count overlapping dates comparing a single date range against multiple date ranges. In this article, I will demonstrate how to count overlapping dates across multiple date ranges.

The date ranges are in columns A and B. The calendar to the right is there so that you can easily verify that the formula is correct.

#### What's on this webpage

## 1. Count the number of overlapping date ranges for each date

The first formula returns an array that counts the number of overlapping date ranges for each date. It is shown in cell range D12:Q12.

The formula returns this array: {1, 2, 1, 3, 1, 2, 2, 1, 0, 1, 1, 4, 3, 1}

Date 2005-01-01 is overlapped once by date range 2005-01-01/2005-01-02. So the first value in the array is 1.

Date 2005-01-02 is overlapped twice by date range 2005-01-01/2005-01-02 and 2005-01-02/2005-01-04. The second value in the array is 2.

...

Date 2005-01-09 is not overlapped at all so the ninth value in the array is 0 (zero).

And so on.., you can verify these numbers against the calendar above.

## 2. Count dates overlapped by two or more date ranges

The second array formula returns an array that indicates if a date is overlapped by two or more date ranges. It is entered in cell range E14:R14.

This formula returns {0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0}

If we sum this array we get the total number of overlapped dates. That value is shown cell D15 and R13.

### 2.1 Explaining formula in cell range D13:Q13

#### Step 1 - Find latest date in end dates

The MAX function returns the largest number from a cell range or array.

MAX($C$3:$C$12)

becomes

MAX({38356; 38360; 38358; 38365; 38366; 38354; 38365; 38356; 38359; 38364})

and returns 38366. Note that these numbers are actually Excel dates, numbers formatted as dates. 38366 is 1/14/2005.

#### Step 2 - Find earliest date in start dates

The MIN function returns the largest number from a cell range or array.

MIN($B$3:$B$12)

becomes

MIN({38354; 38359; 38356; 38362; 38364; 38353; 38364; 38356; 38358; 38364})

and returns 38353.

#### Step 3 - Subtract dates

MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))+1

becomes

38366 - 38353 +1 equals 14.

#### Step 4 - Create a cell reference

The INDEX function is also able to create a cell reference.

INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1)

becomes

INDEX($A:$A, 14)

and returns cell reference A14.

#### Step 5- Concatenate cell references

You need to use the ampersand character & to concatenate strings, however, not necessary in this rare case.

A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1)

returns cell reference A1:A14.

#### Step 6 - Calculate row numbers based on a cell reference

The ROW function returns a row number from a cell reference. It returns multiple row numbers if the cell reference points to a cell range.

ROW(A1:INDEX($A:$A, MAX($B$2:$B$11)-MIN($A$2:$A$11)+1))

becomes

ROW( A1:A14)

and returns {1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14}.

#### Step 5 - Subtract array with 1

ROW(A1:INDEX($A:$A, MAX($B$2:$B$11)-MIN($A$2:$A$11)+1))-1

becomes

{1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14}-1

and returns

{0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13;}

#### Step 6 - Add array to earliest start date

MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1

becomes

38353+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1

becomes

38353 + {0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13;}

and returns

{38353; 38354; 38355; 38356; 38357; 38358; 38359; 38360; 38361; 38362; 38363; 38364; 38365; 38366}

#### Step 7 - Convert vertical array to a horizontal array

The TRANSPOSE function allows you to convert a vertical range to a horizontal range, or vice versa.

TRANSPOSE(array)

TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1)

becomes

TRANSPOSE({38353; 38354; 38355; 38356; 38357; 38358; 38359; 38360; 38361; 38362; 38363; 38364; 38365; 38366})

and returns

{38353, 38354, 38355, 38356, 38357, 38358, 38359, 38360, 38361, 38362, 38363, 38364, 38365, 38366}

#### Step 8 - Test which dates are larger or equal to start dates

TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1)>=$B$3:$B$12

becomes

{38353, 38354, 38355, 38356, 38357, 38358, 38359, 38360, 38361, 38362, 38363, 38364, 38365, 38366}>={38354; 38359; 38356; 38362; 38364; 38353; 38364; 38356; 38358; 38364}

and returns

{FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE;FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE;FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE;FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE;FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE;FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, TRUE;FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE;FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE;FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, TRUE}

#### Step 9 - Test which dates are smaller or equal to end dates

TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1))<=$C$3:$C$12

returns

{TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE;TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE;TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE;TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE;TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE;TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE;TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE;TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE;TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE}

#### Step 10 - Multiply arrays

(TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1)>=$B$3:$B$12)*((TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1))<=$C$3:$C$12)

returns

{0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0;0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0;0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1;1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0;0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0}

#### Step 11 - Create an array of numbers all equal to 1

Exponentiation is a mathematical operation, use the ^ character or the POWER function to calculate the result of exponentiation.

TRANSPOSE($B$3:$B$12^0)

becomes

TRANSPOSE({38354; 38359; 38356; 38362; 38364; 38353; 38364; 38356; 38358; 38364}^0)

becomes

TRANSPOSE({1; 1; 1; 1; 1; 1; 1; 1; 1; 1})

and returns {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}.

#### Step 12 - Evaluate MMULT function

The MMULT function calculates the matrix product of two arrays, an array as the same number of rows as array1 and columns as array2.

MMULT(TRANSPOSE($B$3:$B$12^0), (TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1)>=$B$3:$B$12)*((TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1))<=$C$3:$C$12))

becomes

MMULT({1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0;0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0;0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1;1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0;0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0;0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0})

and returns

{1, 2, 1, 3, 1, 2, 2, 1, 0, 1, 1, 4, 3, 1}

#### Step 13 - Check if value in array is larger than 1

MMULT(TRANSPOSE($B$3:$B$12^0), (TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1)>=$B$3:$B$12)*((TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1))<=$C$3:$C$12))>1

becomes

{1, 2, 1, 3, 1, 2, 2, 1, 0, 1, 1, 4, 3, 1}>1

and returns

{FALSE, TRUE, FALSE, TRUE, FALSE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, FALSE}

#### Step 14 - Convert boolean values

(MMULT(TRANSPOSE($B$3:$B$12^0), (TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1)>=$B$3:$B$12)*((TRANSPOSE(MIN($B$3:$B$12)+ROW(A1:INDEX($A:$A, MAX($C$3:$C$12)-MIN($B$3:$B$12)+1))-1))<=$C$3:$C$12))>1)*1

becomes

{FALSE, TRUE, FALSE, TRUE, FALSE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE, FALSE}*1

and returns

{0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0}.

Functions in this post: MMULT, ROW, INDEX

Interested in learning more about excel formulas? Join my Advanced excel course.

Count unique distinct values that meet multiple criteria

This post demonstrates how to build an array formula that counts unique distinct values based on criteria. What's on this […]

This article describes how to count unique distinct values. What are unique distinct values? They are all values but duplicates are […]

Count Conditionally Formatted cells

This article explains how to count cells highlighted with Conditional Formatting (CF). The image above shows data in cell range […]

Count cells between specified values

This article demonstrates formulas that calculate the number of cells between two values, the first scenario involves two search values […]

Count unique distinct values in two columns

Formula in C12: =SUM(1/COUNTIF($B$3:$B$8, $B$3:$B$8))+SUM(IF(COUNTIF($B$3:$B$8, $D$3:$D$8)=0, 1/COUNTIF($D$3:$D$8, $D$3:$D$8), 0)) How to create an array formula Double press with left mouse […]

Count unique distinct values in a filtered Excel defined Table

This article demonstrates a formula that counts unique distinct values filtered from an Excel defined Table. Debra Dalgleish described in […]

How to count unique distinct values based on a date

The array formula in cell D3 calculates the number of unique distinct items based on the given date in column B. […]

Count unique distinct values within same week, month or year

The array formula in cell E3 counts unique distinct items for all dates within the same week. Example, week 2 […]

Count unique distinct values based on a condition

This article demonstrates how to construct a formula that counts unique distinct values based on a condition. The image above […]

This article demonstrates formulas that count values in cell based on a delimiting character. The image above shows a formula […]

Highlight records based on overlapping date ranges and a condition

adam asks: Hi, I have a situation where I want to count if this value is duplicate and if it […]

Identify overlapping date ranges

The formula in cell F6 returns TRUE if the date range on the same row overlaps another date range in […]

How to calculate overlapping time ranges

I found an old post that I think is interesting to write about today. Think of two overlapping ranges, it […]

Identify rows of overlapping records

This article demonstrates a formula that points out row numbers of records that overlap the current record based on a […]

Count overlapping days in multiple date ranges

The MEDIAN function lets you count overlapping dates between two date ranges. If you have more than two date ranges […]

Count overlapping days across multiple date ranges

This post demonstrates a formula in cell D16 that counts overlapping dates across multiple date ranges. The date ranges are […]

Find empty dates in a set of date ranges

The formula in cell B8, shown above, extracts dates not included in the specified date ranges, in other words, dates […]

Highlight date ranges overlapping selected record [VBA]

This article demonstrates event code combined with Conditional Formatting that highlights overlapping date ranges based on the selected date range. […]

Working with overlapping date ranges

This article demonstrates formulas that calculate the number of overlapping ranges for all ranges, finds the most overlapped range and […]

### 5 Responses to “Count overlapping days in multiple date ranges, part 2”

### Leave a Reply to Trish

### How to comment

**How to add a formula to your comment**

<code>Insert your formula here.</code>

**Convert less than and larger than signs**

Use html character entities instead of less than and larger than signs.

< becomes < and > becomes >

**How to add VBA code to your comment**

[vb 1="vbnet" language=","]

Put your VBA code here.

[/vb]

**How to add a picture to your comment:**

Upload picture to postimage.org or imgur

Paste image link to your comment.

**Contact Oscar**

You can contact me through this contact form

Hi Oscar,

Thanks for your knowledge sharing and really helpful!

You have mentioned the overlapping date within a single month. My question is how can we highlight the overlapping dates for 2 months. Kindly find the details below for your reference.

Date Format is in (MM/DD/YYYY)

Start - 03/28/2016 - End - 04/05/2016

Start - 04/25/2016 - End - 05/10/2016

I need your help in this issue. It will be great if I get the solution for this and the same will reduce my work upto 50%. Requesting you to provide me the solution for my query.

Regards

Sam Fredy. P

Hi Oscar,

Please help. Awaiting for your positive reply.

Regards

Sam

Hi Oscar,

Pls help me for my query.

Regards

Sam

My question is probably better suited here (I had initially posted in it Part 1). For this example, I want to find the maximum number of overlaps that occurred with a set of date ranges (i.e. in this example above, it would be four (or another way of looking at it is I want the Max value of Row 12).

This is so close to what I want. However, what I would LOVE to see in column "R" is the total number of days that one date overlaps all others.

For instance, the date range on row has 2 days that overlap 3 other date ranges. I would like to see the formula for calculating that 2 days in Column "R"

Then I can do a "Countifs" for the number days that overlap with other date ranges where the same "resource" has been assigned.

Is this possible?