Author: Oscar Cronquist Article last updated on October 09, 2018

The worksheet above shows four different time ranges in column B and C, the formula in cell C10 counts the number of overlapping minutes.

The formula uses the earliest and latest date and time value in column B and C as the range to count overlapping minutes.

Array formula in cell C10:

=SUM((MMULT(TRANSPOSE($B$3:$B$6^0), (TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440)>=$B$3:$B$6)*((TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440))<$C$3:$C$6))>1)*1)

To enter an array formula, type the formula in a cell then press and hold CTRL + SHIFT simultaneously, now press Enter once. Release all keys.

The formula bar now shows the formula with a beginning and ending curly bracket telling you that you entered the formula successfully. Don't enter the curly brackets yourself.

Explaining formula in cell C10

The INDEX function allows you to create an array of values, in this case, minute intervals.

MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440

returns

{43101.25, 43101.2506944444, 43101.2513888889, 43101.2520833333, 43101.2527777778, 43101.2534722222, 43101.2541666667, 43101.2548611111, 43101.2555555556, 43101.25625, 43101.2569444444}

Now check if these minute intervals are between or equal to each date and time range.

(TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440)>=$B$3:$B$6)*((TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440))<$C$3:$C$6)

returns

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

The MMULT function allows you to add these values column by column.

MMULT(TRANSPOSE($B$3:$B$6^0), (TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440)>=$B$3:$B$6)*((TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440))<$C$3:$C$6))

becomes

MMULT(TRANSPOSE($B$3:$B$6^0), {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0; 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0})

becomes

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

and returns

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

The following picture shows the array and what the MMULT function returns.

A value larger than 1 indicates an overlapping time value.

MMULT(TRANSPOSE($B$3:$B$6^0), (TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440)>=$B$3:$B$6)*((TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440))<=$C$3:$C$6))>1

becomes

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

and returns

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

Lastly, multiply with 1 to convert boolean values to numerical values and then sum the numbers.

SUM((MMULT(TRANSPOSE($B$3:$B$6^0), (TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440)>=$B$3:$B$6)*((TRANSPOSE(MIN($B$3:$B$6)+(ROW(A1:INDEX($A:$A, (MAX($C$3:$C$6)-MIN($B$3:$B$6))*1440+1))-1)/1440))<=$C$3:$C$6))>1)*1)

becomes

SUM({FALSE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE, FALSE}*1)

becomes

SUM({0,1,1,1,1,1,1,1,0,1,0})

and returns 8.

The picture above shows you a different setup, it allows you to use a smaller range than the min and max date and time in B3:C5.

Formula in cell C14:

=SUM((MMULT(TRANSPOSE($B$3:$B$5^0), (TRANSPOSE($B$9+(ROW(A1:INDEX($A:$A, ($C$9-$B$9)*1440+1))-1)/1440)>=$B$3:$B$5)*((TRANSPOSE($B$9+(ROW(A1:INDEX($A:$A, ($C$9-$B$9)*1440+1))-1)/1440))<$C$3:$C$5))>0)*1)

The ROW function limits the use of these formulas, if you have a range larger than 1,048,576 minutes, which is the same as the number of rows in a worksheet, you will need another solution than the one presented here.

Download Excel *.xlsx file

How to count overlapping timev3.xlsx

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