Array in excel with example

In Excel, an Array Formula allows you to do powerful calculations on one or more value sets. The result may fit in a single cell or it may be an array. An array is just a list or range of values, but an Array Formula is a special type of formula that must be entered by pressing Ctrl+Shift+Enter. The formula bar will show the formula surrounded by curly brackets {=…}.

Array formulas are frequently used for data analysis, conditional sums and lookups, linear algebra, matrix math and manipulation, and much more. A new Excel user might come across array formulas in other people’s spreadsheets, but creating array formulas is typically an intermediate-to-advanced topic.

Download the Example File (ArrayFormulas.xlsx)

Topics and Examples in This Article:

• Entering an Array Formula
• Using Array Constants
• A Simple Array Formula Example
• Entering a Multi-Cell Array Formula
• Nested IF Array Formulas
• COUNTIF Alternative: SUM-Boolean Array Formulas
• Multi-Criteria Boolean Array Formulas
• Sequential Number Arrays (1,2,3,…)
• Formulas for Matrices: MUNIT, MMULT, TRANSPOSE, etc.
• Other Array Formula Examples

Watch the Intro Video

Entering and Identifying an Array Formula

1. When using an Array Formula, you press Ctrl+Shift+Enter instead of just Enter after entering or editing the formula. This is why array formulas are often called CSE formulas.
2. An Array Formula will show curly brackets or braces around the formula in the Formula Bar like this: {=SUM(A1:A5*B1:B5)}
3. Array Constants (arrays «hard-coded» into formulas) are enclosed in braces { } and use commas to separate columns, and semi-colons to separate rows, like this 2×3 array: {1, 1, 1; 2, 2, 2}
4. If an Array Formula returns more than one value (a multi-cell array formula), first select a range of cells equal to size of the returned array, then enter your formula.
5. To select all the cells within a multi-cell array: Press F5 > Special > Current Array.

! Every time you edit an Array Formula, you must remember to press Ctrl+Shift+Enter afterward. If you forget to, the formula may return an error without you realizing it.

NOTE Google Sheets uses the ARRAYFORMULA function instead of showing the formula surrounded by braces. It is not necessary to press Ctrl+Shift+Enter in Google Sheets, but if you do, ARRAYFORMULA( is added to the beginning of the formula.

Using Array Constants in Formulas

Many functions allow you use array constants like {1,2,6,12} as arguments within formulas. An example that I often use in my yearly calendar templates returns the weekday abbreviation for a given date. The nice thing about this formula is that you can choose whether to display a single character or two characters.

=INDEX({"Su";"M";"Tu";"W";"Th";"F";"Sa"},WEEKDAY(theDate,1))

This formula is not technically an Array Formula because you don’t enter it using Ctrl+Shift+Enter. Using a hard-coded array within a formula does not necessarily require using Ctrl+Shift+Enter.

TIP If you are going to use the array constant in multiple formulas, you may want to first create a Named Constant. Go to Formulas > Name Manager > New Name, enter a descriptive name like payment_frequency and enter ={1,2,6,12} into the Refers To field. You can use the name within your formulas. If you ever want to change the values within that array constant, you only need to change it one place (within the Name Manager).

A Simple Array Formula Example

To start out, I will show how an array formula works using a very basic example. Let’s say that I have a list of tasks, the number of days each of those tasks will take, and a column for the percent complete. I want to know the total number of days that have been completed.

Without an array formula, you would create another column called «Completed» and multiply the number of days by the % complete, and copy the formula down. Then I would use SUM to total the number of days completed, like the image below:

With an array formula, you can do essentially the same thing without having to create the extra column. Within a single cell, you can calculate the total days completed as =SUM(D18:D22*E18:E22), remembering to press Ctrl+Shift+Enter because it is an array formula.

{ =SUM(D18:D22*E18:E22) }

Evaluation Steps
Step 1: =SUM( {10;5;8;3;12} * {0.5;0.2;0.07;0.5;0.09} )
Step 2: =SUM( {10*0.5;5*0.2;8*0.7;3*0.5;12*0.09} )
Step 3: =SUM( {5;1;0.56;1.5;1.08} )
Step 4: =9.14

In this and other examples, I’ve shown the evaluation steps below the formula so that you can see how the formula works. You don’t actually type the curly brackets { }, but in this article I will surround all array formulas with brackets to indicate that they are entered as CSE formulas.

In the evaluation steps shown in the above example, you’ll see that Excel is multiplying each element of the first array by the corresponding element in the second array, and then SUM adds the results.

NOTE It turns out that this particular example can be used to show how the SUMPRODUCT function works, but the SUMPRODUCT function deserves its own article.

To take this example just a bit further, if all we wanted to know was the Total Percent Complete for the entire project, we can divide the total days completed (9.14) by the total days (38) all within a single array formula, and we don’t need column F at all (as shown in the image below).

This example is an example of a single-cell array formula, meaning that the formula is entered into a single cell.

Entering a Multi-Cell Array Formula

Whenever your array formula returns more than one value, if you want to display more than just the first value, you need to select the range of cells that will contain the resulting array before entering your formula. Doing this will result in a multi-cell array formula, meaning that the result of the formula is a multi-cell array.

Using the same example as above, we could use an array formula in the Completed column to calculate Days * Percent Complete. First, select cells F18:F22, then press = and enter the formula, followed by Ctrl+Shift+Enter (CSE). The image below is what it will look like just before you press CSE.

You can edit a multi-cell array formula by selecting any of the cells in the array and then updating the formula and pressing Ctrl+Shift+Enter when you are done. However, you can’t use this technique to modify the size of the array.

«You can’t change part of an array» — This is the warning or error you will get if you try to insert rows or columns or change individual cells within a multi-cell array.

Using multi-cell array formulas can make it more difficult to customize a spreadsheet because to change the size of the array requires that you (1) delete the formula (after selecting all the cells of the array), (2) select the new range of cells, and (3) re-enter the array formula. TIP: Make sure to copy your original formula before deleting it. Then, when you re-enter the formula, you can paste it and modify the ranges.

Nested IF Array Formulas

A nested IF array formula can be very powerful and is probably one of the more common uses for array formulas in Excel. Although Excel provides the SUMIF and COUNTIF and AVERAGEIF functions, they don’t allow as much freedom as a nested IF array formula.

MAX-IF Array Formula

Older versions of Excel do not have the MAXIFS or MINIFS functions, so let’s create our own MAX-IF formula. When we use hyphens to name a formula, it usually means that we’re nesting the functions (IF within MAX in this case).

Let’s say that I have the following contact and sales log and I want a formula that will tell me when I last contacted Bob (cell H51).

Using MAX on the date range will give me that latest date (9/10/2017), but I only want to include the rows where the contact is Bob. So, I’ll use the MAX-IF array formula:

{ =MAX(IF(contact_range="Bob",date_range)) }

Evaluation Steps
Step 1: =MAX(IF({"Jim";"Bob";"Jim";"Bob";"Jim"}="Bob", date_range ))
Step 2: =MAX(IF({FALSE;TRUE;FALSE;TRUE;FALSE}, date_range ))
Step 3: =MAX( {FALSE,2/25/2017,FALSE,8/5/2017,FALSE} )
Step 4: =8/5/2017

LARGE-IF Array Formula

The LARGE and SMALL functions come in handy when you want to find the value that is perhaps the 2nd largest or 2nd smallest.

The following function will return the second largest sale where the contact is Jim.

{ =LARGE(IF(contact_range="Jim",sale_range),2) }

SMALL-IF Array Formula

This function returns the second smallest sale where the contact is Jim.

{ =SMALL(IF(contact_range="Jim",date_range),2) }

The LARGE and SMALL functions can be used for sorting arrays. More on that later. Hopefully, Excel will introduce a SORT function soon (Google Sheets has already done that).

The SMALL-IF formula can be used in combination with INDEX to do a lookup a value based on the Nth Match.

SUM-IF Array Formula

Yes, there is already a SUMIF function that is generally better than using an array formula, but we’ll be getting into more advanced SUM-IF array formulas, so it’s useful to see the simple example:

{ =SUM(IF(contact_range="Jim",sales_range)) }

More Reading: Chip Pearson provides some great examples of ways to use nested IF functions within the SUM and AVERAGE functions to ignore errors and zero values. See Chip Pearson’s article.

COUNTIF Alternative: SUM-Boolean Array Formulas

Although there is already a COUNTIF function, the criteria available in the COUNTIF family of functions is limited. An alternative method is to do a SUM of boolean (TRUE/FALSE) results that have been converted to 0s and 1s (FALSE=0, TRUE=1). Boolean results can be converted to 0s and 1s by adding +0, multiplying by *1 and by using double negation.

SUM-ISERROR: Count the number of Error values in a range

{ =SUM(1*ISERROR(range)) }
{ =SUM(0+ISERROR(range)) }
{ =SUM(--ISERROR(range)) }

Evaluation Steps
Step 1: =SUM( 1*{FALSE,TRUE,TRUE,FALSE,TRUE} )
Step 2: =SUM( {0,1,1,0,1} )
Step 3: =3

SUM-ISBLANK: Count the number of Blank values in a range

{ =SUM(--ISBLANK(range)) }

Remember: A formula that returns an empty «» string is considered NOT blank.

SUM-NOT-ISBLANK: Count the number of Non-Blank values in a range

{ =SUM(--NOT(ISBLANK(range)) }

Multi-Criteria Boolean Array Formulas

The AND and OR functions return only a single value, even when they contain multiple arrays, so we don’t generally use them within array formulas.

For multiple-criteria logical array formulas, such as SUM-IF between two dates, you need to do the boolean logic by adding boolean values for «or» conditions and by multiplying boolean values for «and» conditions.

SUM-IF Between Two Dates

Yes, SUMIFS would be easier, but let’s assume we are using an older version of Excel. Referring back to the Contact and Sales log, we’ll sum all of the Sales between 2/1/2017 and 9/1/2017, meaning that Date >= 2/1/2017 AND Date <= 9/1/2017.

{ =SUM(IF((date_range>=start)*(date_range<=end), sum_range) ) }

Evaluation Steps
Step 1: SUM(IF({FALSE,TRUE,TRUE,TRUE,TRUE}*{TRUE,TRUE,TRUE,TRUE,FALSE},sum_range))
Step 2: SUM(IF({0,1,1,1,0},sum_range))
Step 3: SUM({FALSE,300,500,0,FALSE})
Step 4: 800

In this case we don’t need to use 1*(…) to convert the boolean values, because the boolean values are converted to 0s and 1s automatially when we multiply the two arrays together. The IF function in Excel treats the value 0 as FALSE and all other values as TRUE.

Overlapping OR Conditions

To demonstrate a logical OR condition, we’ll sum the sales where Name = «Bob» OR Date > 7/1/2017. An «or» condition is true when one or more of the conditions is true, so we check whether the sum of the expressions is greater than 0.

{ =SUM(IF( ((contact_range="Bob")+(date_range>=date))>0, sum_range) ) }

Evaluation Steps
Step 1: SUM(IF(({FALSE,TRUE,FALSE,TRUE,FALSE}+{FALSE,FALSE,TRUE,TRUE,TRUE})>0,sum_range))
Step 2: SUM(IF({0,1,1,2,1}>0,sum_range))
Step 3: SUM(IF({FALSE,TRUE,TRUE,TRUE,TRUE},sum_range))
Step 4: SUM({FALSE,300,500,0,200})
Step 5: 1000

Using this approach, you can create multiple-criteria equivalents for MAX-IF, LARGE-IF, and other array formulas.

Sequential Number Arrays

For many array formulas, you will need to use an array of sequential numbers like {1; 2; 3; … n}. You can return a sequential number array from 1 to n using this formula:

{ =ROW(1:n) }
-or-
{ =ROW(OFFSET($A$1,0,0,n,1)) }

Important: Although it doesn’t matter what is contained in cell A1, if you delete the cell (by removing row 1 or column A for example), insert a row above or a column to the left of cell A1, or cut and paste cell A1 to a different location, your array formula will be messed up. To avoid this problem, use the INDIRECT function:

{ =ROW(INDIRECT("1:"&n)) }
-or-
{ ROW(OFFSET(INDIRECT("A1"),0,0,n,1)) }

NOTE The OFFSET and INDIRECT function are volatile functions. If calculation speed becomes a problem due to these formulas, you could either use ROW(1:n) and risk having row 1 removed, or you could reference a hidden or protected worksheet using =ROW(Sheet4!1:n)

Variant #1: Create a Sequence of Whole Numbers from i to j

If you want to hard-code the values for i and j into the formula, an array formula such as ROW(4:8) may work fine to create the array {4;5;6;7;8}. If you want the formula to use cell references for i and j, you can use INDIRECT like this:

A1 = 4
B1 = 8
{ =ROW(INDIRECT(A1&":"&B1)) }

Result: {4;5;6;7;8}

Variant #2: Create an n x 1 Vector of Whole Numbers Starting From s

You can use this technique when you want to specify the length of the number array instead of the end value. To create the array {s; s+1; s+2; … s+n-1} use

s = 4
n = 7
{ =s+ROW(OFFSET(INDIRECT("A1"),0,0,n,1))-1 }
   -or-
{ =ROW(INDIRECT(s&":"&s+n-1)) }

Result: {4;5;6;7;8;9;10}

Variant #3: Sequence of Dates Between START and END (inclusive)

To create an array of dates from start through end (assuming start and end are cells containing date values), remember that date values are stored as whole numbers. If they are indeed date values and not date-time values, you can use:

start_date = 1/1/2018
end_date = 1/5/2018
{ =ROW(INDIRECT(start_date&":"&end_date)) }

Result: {43101;43102;43103;43104;43105}

The result shows the numeric values for 1/1/2018, 1/2/2018, etc. You can format the results using whatever date format you want. If your start and end dates might be date-time values, then strip the time portion off of the number like this:

{ =ROW(INDIRECT(INT(start_date)&":"&INT(end_date)) }

Variant #4: Create an n x 1 Vector of Sequential Powers of 10

To create the array {1; 10; 100; 1000; … 10^(n-1)} use

{ =10^(ROW(OFFSET(INDIRECT("A1"),0,0,n,1))-1) }
-or-
{ =10^(ROW(INDIRECT("1:"&n))-1) }

Formulas for Matrices

Excel contains some key functions for working with matrices:

• MUNIT(m): Creates an Identity matrix of size m x m
• MMULT(A,B): Uses matrix multiplication to multiply an n x k matrix A by a k x m matrix B resulting in an array of size n x m.
• TRANSPOSE(A): Switches rows to columns or vice versa, and can be used for more than just numbers.
• MDETERM(A): Calculates the determinant of a matrix A.
• MINVERSE(A): Calculates the inverse of the matrix A (if possible).
• INDEX(A,n) or INDEX(A,0,m): Returns either row n or column m of matrix A.

NOTE Excel does a great job of displaying data, but if you need to do a lot of statistical analysis and linear algebra, other tools such as Python, R, and Matlab may be better.

Element-Wise Multiplication of 2 Matrices

You can perform element-wise multiplication of 2 matrices by simply multiplying two ranges and entering the function as an Array Formula. For example, the formula ={1,2;3,4}*{a,b;c,d} would return the array {1*a,2*b;3*c,4*d}. If one matrix has more columns or rows than the other, those values will be truncated from the result.

Creating the ONES Vector and ONES Matrix

The ones vector j={1;1;1…} and the ones matrix J={1,1;1,1} are very useful in linear algebra and array formulas. The image below shows an example using the MUNIT function to create the Identity matrix I, the ones vector j, and the ones matrix J.

A simple way to create an n x n ones matrix (J) is to multiply the identity matrix by 0 and add 1, like this:

{ =1+0*MUNIT(n) }

The ones vector (j) of size n x 1 can be created by using INDEX to return the first column of the ones matrix, like this:

{ =INDEX(1+0*MUNIT(n),0,1) }

In older versions of Excel that don’t support the MUNIT function, you can create the ones vector, ones matrix and identity matrix using these formulas:

j =(1+0*ROW(INDIRECT("1:"&n)))
J =IF(ISERROR(OFFSET(INDIRECT("A1"),0,0,n,n)),1,1)
I =IF( ROW(OFFSET(INDIRECT("A1"),0,0,n,n)) = COLUMN(OFFSET(INDIRECT("A1"),0,0,n,n)), 1, 0)

Repeating Rows or Columns to Create a Matrix

Sometimes you may need to form a matrix by repeating a row or column. This can be done using MMULT and the ones vector.

If you want to create a matrix with n rows by repeating row={1, 2, 3}, use the array formula =MMULT(j,row) where j is size n x 1.

{ =MMULT( INDEX(1+0*MUNIT(n),0,1), row) }

If you want to create a matrix with k columns by repeating col={1;2;3}, use the array formula =MMULT(col,TRANSPOSE(j)) where j is size k x 1.

{ =MMULT(col, TRANSPOSE(INDEX(1+0*MUNIT(k),0,1)) ) }

ROW or COLUMN Sums using the ONES Vector

It turns out that the ONES vector is very important in statistics for performing a very simple matrix operation: summing the rows or columns. Let’s say you have a range of size n (rows) x k (columns). You could either use the SUM function separately for each row or column, or you could use array formulas.

Column-Sum: To the sum the values within each COLUMN of the matrix and return the sums as a 1 x n array (or row vector), use

ones_vector =INDEX(1+0*MUNIT(ROWS(range)),0,1)
column_sum =MMULT(TRANSPOSE(ones_vector),range)

Row-Sum: To sum the values within each ROW of the matrix and return the sums as a k x 1 array (or column vector), use

ones_vector =INDEX(1+0*MUNIT(COLUMNS(range)),0,1)
row_sum =MMULT(range,ones_vector)

Creating a DIAGONAL Matrix

Element-wise multiplication of matrices can be used to create a Diagonal matrix. A Diagonal matrix is a special matrix where all of the off-diagonal terms are zeros. To create the Diagonal matrix, you multiply the matrix by the Identity matrix of the same size:

Diagonal =A*MUNIT(ROWS(A))

Many programs (but not Excel) include a function like diag(matrix) which returns an n x 1 vector containing the diagonal terms of an n x n matrix. To return the diagonal as a vector, you can use the row-sum operation on the Diagonal like this:

diag(A) =MMULT(A*MUNIT(ROWS(A)),(1+0*ROW(INDIRECT("1:"&ROWS(A)))))

Find the TRACE of a Square Matrix

The trace of a square matrix is just the sum of the diagonal elements. Therefore, the formula for calculating the trace is just:

trace(A) =SUM( A*MUNIT(ROWS(A)) )

Other Array Formula Examples

Linear Regression

The trend lines in an Excel chart allow you to do simple linear regression, but you can also do linear regression in Excel using matrix and array functions. It’s much easier to just use the LINEST function, but for fun I give the general formula for calculating the b matrix (the least squares estimators) when you have the y and X matrix. Or in other words, if you want to solve for b starting from y=Xb, you can do that using the formula b=(X‘X)^-1X‘y which in Excel is:

{ =MMULT(MMULT(MINVERSE(MMULT(TRANSPOSE(x),x)),TRANSPOSE(x)),y) }

Alternate XNPV Function

If for some reason you don’t like Excel’s XNPV function or for some reason you need to use 360 days in a year instead of 365, you can use the following array formula in place of XNPV, where r is the discount rate.

{ =SUM(values_range/((1+r)^((date_range-INDEX(date_range,1))/365))) }

Running XIRR Formula

My Investment Tracker calculates an annualized compounded rate of return using a running XIRR array formula.

Some References for Array Formulas in Excel

• Guidelines and Examples of Array Formulas at support.office.com
• Array Formulas at cpearson.com — Some detailed information about using array formulas in Excel, along with some example array functions.
• Matrix Functions in Excel at bettersolutions.com — Examples showing the use of MDETERM, MINVERSE, MMULT, and TRANSPOSE.
• Using Excel to find Eigenvalues and Eigenvectors
• A.C.Rencher, Methods of Multivariate Analysis, John Wiley & Sons, Inc.: New York, 1995.

The array of Excel functions allows you to solve complex tasks in automatically at the same time. We cannot complete the same tasks through the usual functions.

In fact, this is a group of functions that simultaneously process a group of data and immediately produce a result. Let’s consider in detail work with arrays of functions in Excel.



Types of Excel functions

Array is a data grouped together. In this case, the group is an array of functions in Excel. Any table that we compose and fill in Excel can be called an array. Example:

Depending on the location of the elements, the arrays are distinguished:

• One-dimensional (data is in ONE line or in ONE column);
• Two-dimensional (SEVERAL lines and columns, matrix).

One-dimensional arrays are:

• Horizontal (data in a row);
• Vertical (data in a column).

Note. Two-dimensional Excel arrays can take several sheets at once (these are hundreds and thousands of data).

Array formula allows you to process data from this array. It can return one value or result in an array (set) of values.

With the help of array formulas it is real to:

• Count the number of characters in a certain range;
• Summarize only those numbers that correspond to the given condition;
• Summarize all n values in a certain range.

When we use array formulas, Excel takes into account the range of values not as individual cells, but as a single data block.



Array formulas syntax

We use the formula of an array with a range of cells and with a separate cell. In the first case, we find the subtotals for the «To pay» «» column. In the second — the total amount of utility payments.

1. We select the range E3: E8.
2. Enter the following formula in the formula row: = C3: C8 * D3: D8.



3. Press the keys simultaneously: Ctrl + Shift + Enter. The subtotals are calculated:

The formula after pressing Ctrl + Shift + Enter was in curly brackets. It was automatically inserted into each cell of the selected range.

If you try to change the data in any cell in the «To pay» column, nothing happens. The formula in the array protects range values from changes. A corresponding entry appears on the screen:

Consider other examples of using the functions of an Excel array — calculate the total amount of utility payments using a single formula.

1. Select the cell E9 (opposite the «Total»).
2. We introduce a formula of the form:
3. Press the key combination: Ctrl + Shift + Enter. Result:

The formula of the array in this case replaced two simple formulas. This is a shortened version, which contains all the necessary information for solving a complex problem.

Arguments for a function are one-dimensional arrays. The formula looks at each of them individually, performs user-defined operations, and generates a single result.

Consider the syntax:

Working functions with Excel array

Let’s guess that it is planned to increase utility payments in 10% the next month. If we introduce the usual formula for the total is =SUM((C3:C8*D3:D8)+10%), then we are unlikely to get the expected result. We need each argument to increase in 10%. For the program to understand this, we use the function as an array.

1. Let’s have a look how the «И» «AND» operator works in the array function. We need to find out how much we pay for the water, hot and cold. Function:

   The total is 86.46$.



2. The Sort functions in the array formula. Sort the amounts to be paid in ascending order. For the sorted data list, create a range. Let’s select it (F3:F7). In the formula bar, we enter

   Press Ctrl + Shift + Enter.



3. The transported matrix. There is a special Excel function for working with two-dimensional arrays. The «ТРАНСП» function returns several values at once. It converts a horizontal matrix to a vertical matrix and vice versa. Select the range of cells where the number of rows equals to the number of columns in the table with the original data. And the number of columns equals to the number of rows in the source array. Select range A9:F10. We introduce the formula:

   Press Ctrl + Shift + Enter. This results in an «inverted» data set.



4. Search for the average without taking into account zeros. If we use the standard «AVERAGE» function, we get «0» as a result. And it will be correct. Therefore, we insert an additional condition into the formula:

We get:

A common mistake when working with arrays of functions is NOT to press the code combination «Ctrl + Shift + Enter» (never forget this key combination). This is the most important thing to remember when processing large amounts of information. Correctly entered function performs the most complicated tasks.

Download array formula examples

Во время работы с таблицами Excel довольно часто приходится оперировать с целыми диапазонами данных. При этом некоторые задачи подразумевают, что вся группа ячеек должна быть преобразована буквально в один клик. В Экселе имеются инструменты, которые позволяют проводить подобные операции. Давайте выясним, как можно управлять массивами данных в этой программе.

Операции с массивами

Массив – это группа данных, которая расположена на листе в смежных ячейках. По большому счету, любую таблицу можно считать массивом, но не каждый из них является таблицей, так как он может являться просто диапазоном. По своей сущности такие области могут быть одномерными или двумерными (матрицы). В первом случае все данные располагаются только в одном столбце или строке.

Во втором — в нескольких одновременно.

Кроме того, среди одномерных массивов выделяют горизонтальный и вертикальный тип, в зависимости от того, что они собой представляют – строку или столбец.

Нужно отметить, что алгоритм работы с подобными диапазонами несколько отличается от более привычных операций с одиночными ячейками, хотя и общего между ними тоже много. Давайте рассмотрим нюансы подобных операций.

Создание формулы

Формула массива – это выражение, с помощью которого производится обработка диапазона с целью получения итогового результата, отображаемого цельным массивом или в одной ячейке. Например, для того, чтобы умножить один диапазон на второй применяют формулу по следующему шаблону:

=адрес_массива1*адрес_массива2

Над диапазонами данных можно также выполнять операции сложения, вычитания, деления и другие арифметические действия.

Координаты массива имеют вид адресов первой её ячейки и последней, разделенные двоеточием. Если диапазон двумерный, то первая и последняя ячейки расположены по диагонали друг от друга. Например, адрес одномерного массива может быть таким: A2:A7.

А пример адреса двумерного диапазона выглядит следующим образом: A2:D7.

1. Чтобы рассчитать подобную формулу, нужно выделить на листе область, в которую будет выводиться результат, и ввести в строку формул выражение для вычисления.



2. После ввода следует нажать не на кнопку Enter, как обычно, а набрать комбинацию клавиш Ctrl+Shift+Enter. После этого выражение в строке формул будет автоматически взято в фигурные скобки, а ячейки на листе будут заполнены данными, полученными в результате вычисления, в пределах всего выделенного диапазона.

Изменение содержимого массива

Если вы в дальнейшем попытаетесь удалить содержимое или изменить любую из ячеек, которая расположена в диапазоне, куда выводится результат, то ваше действие окончится неудачей. Также ничего не выйдет, если вы сделаете попытку отредактировать данные в строке функций. При этом появится информационное сообщение, в котором будет говориться, что нельзя изменять часть массива. Данное сообщение появится даже в том случае, если у вас не было цели производить какие-либо изменения, а вы просто случайно дважды щелкнули мышью по ячейке диапазона.

Если вы закроете, это сообщение, нажав на кнопку «OK», а потом попытаетесь переместить курсор с помощью мышки, или просто нажмете кнопку «Enter», то информационное сообщение появится опять. Не получится также закрыть окно программы или сохранить документ. Все время будет появляться это назойливое сообщение, которое блокирует любые действия. А выход из ситуации есть и он довольно прост

1. Закройте информационное окно, нажав на кнопку «OK».



2. Затем нажмете на кнопку «Отмена», которая расположена в группе значков слева от строки формул, и представляет собой пиктограмму в виде крестика. Также можно нажать на кнопку Esc на клавиатуре. После любой из этих операций произойдет отмена действия, и вы сможете работать с листом так, как и прежде.

Но что делать, если действительно нужно удалить или изменить формулу массива? В этом случае следует выполнить нижеуказанные действия.

1. Для изменения формулы выделите курсором, зажав левую кнопку мыши, весь диапазон на листе, куда выводится результат. Это очень важно, так как если вы выделите только одну ячейку массива, то ничего не получится. Затем в строке формул проведите необходимую корректировку.



2. После того, как изменения внесены, набираем комбинацию Ctrl+Shift+Esc. Формула будет изменена.

1. Для удаления формулы массива нужно точно так же, как и в предыдущем случае, выделить курсором весь диапазон ячеек, в котором она находится. Затем нажать на кнопку Delete на клавиатуре.



2. После этого формула будет удалена со всей области. Теперь в неё можно будет вводить любые данные.

Функции массивов

Наиболее удобно в качестве формул использовать уже готовые встроенные функции Excel. Доступ к ним можно получить через Мастер функций, нажав кнопку «Вставить функцию» слева от строки формул. Или же во вкладке «Формулы» на ленте можно выбрать одну из категорий, в которой находится интересующий вас оператор.

После того, как пользователь в Мастере функций или на ленте инструментов выберет наименование конкретного оператора, откроется окно аргументов функции, куда можно вводить исходные данные для расчета.

Правила ввода и редактирования функций, если они выводят результат сразу в несколько ячеек, те же самые, что и для обычных формул массива. То есть, после ввода значения обязательно нужно установить курсор в строку формул и набрать сочетание клавиш Ctrl+Shift+Enter.

Урок: Мастер функций в Excel

Оператор СУММ

Одной из наиболее востребованных функций в Экселе является СУММ. Её можно применять, как для суммирования содержимого отдельных ячеек, так и для нахождения суммы целых массивов. Синтаксис этого оператора для массивов выглядит следующим образом:

=СУММ(массив1;массив2;…)

Данный оператор выводит результат в одну ячейку, а поэтому для того, чтобы произвести подсчет, после внесения вводных данных достаточно нажать кнопку «OK» в окне аргументов функции или клавишу Enter, если ввод выполнялся вручную.

Урок: Как посчитать сумму в Экселе

Оператор ТРАНСП

Функция ТРАНСП является типичным оператором массивов. Она позволяет переворачивать таблицы или матрицы, то есть, менять строки и столбцы местами. При этом она использует исключительно вывод результата в диапазон ячеек, поэтому после введения данного оператора обязательно нужно применять сочетание Ctrl+Shift+Enter. Также нужно отметить, что перед введением самого выражения нужно выделить на листе область, у которой количество ячеек в столбце будет равно числу ячеек в строке исходной таблицы (матрицы) и, наоборот, количество ячеек в строке должно равняться их числу в столбце исходника. Синтаксис оператора следующий:

=ТРАНСП(массив)

Урок: Транспонирование матриц в Excel

Урок: Как перевернуть таблицу в Экселе

Оператор МОБР

Функция МОБР позволяет производить вычисление обратной матрицы. Все правила ввода значений у этого оператора точно такие же, как и у предыдущего. Но важно знать, что вычисление обратной матрицы возможно исключительно в том случае, если она содержит равное количество строк и столбцов, и если её определитель не равен нулю. Если применять данную функцию к области с разным количеством строк и столбцов, то вместо корректного результата на выходе отобразится значение «#ЗНАЧ!». Синтаксис у этой формулы такой:

=МОБР(массив)

Для того чтобы рассчитать определитель, применяется функция со следующим синтаксисом:

=МОПРЕД(массив)

Урок: Обратная матрица в Excel

Как видим, операции с диапазонами помогают сэкономить время при вычислениях, а также свободное пространство листа, ведь не нужно дополнительно суммировать данные, которые объединены в диапазон, для последующей работы с ними. Все это выполняется «на лету». А для преобразования таблиц и матриц только функции массивов и подходят, так как обычные формулы не в силах справиться с подобными задачами. Но в то же время нужно учесть, что к подобным выражениям применяются дополнительные правила ввода и редактирования.

Excel is among the most powerful and widely used spreadsheet tools which eases organizing numbers and data within the sheets with pre-built formulas and functions. In this article, we are going to study Array Formulas. Arrays are one of them. Using Excel Array Formulas, make it super easy to handle a lot of data. Before understanding and using the Array formulas, let’s first understand what is Array in Excel?

Array in Excel

An Array in Excel is the structure that holds a collection of data. These data can be in the form of numbers or texts. There could be an array of 1-D or 2-D as well in Excel. For example, the array of fruits in excel would be written something like this:-

{“Apple”, “Banana”, “Grapes”, “Guava”}

We can directly enter it into the sheet by selecting the cells where you want to enter the data and then writing the array preceded by an “=” sign.  After these press Ctrl+Shift+Enter. For example, let’s enter these values in cells A1 to D1.

The array created here is a horizontal array. You can also create a vertical array by changing the selected cells. You can create an array by specifying the starting and the ending positions, for example, if you wish to make an array of elements between A1 to F1 then you can write A1:F1. Now. let’s move to array formulas.

Array formulas

Array formulas enable to process of several values and give several outputs. In a simple world, it can do multiple calculations and reduce a lot of human efforts. In other words, we can say that it solves array calculations and give an array as output too. Let’s understand more of them with an example, of students with their test marks,

Here, we have used a formula to evaluate the result in the ‘Total’ field. For inserting the formula, click on the cell where you want to store the answer and write the formula. Now, let’s try to calculate the same for all students

For calculating the total for all the students, select the field where you want to store them, now select the range, and insert the formula. Array formulas are available in every version of Excel, so you don’t worry about your excel version. There are hundreds of operations possible using array formulas, which we will discuss in this article later. But before proceeding let’s understand what is the need to use an array formula.

Why use an Array Formula?

Array formulas are to most powerful yet most easy-to-use calculation tools which could be used to perform complex calculations and take place of hundreds of formulas with a single formula. You can further specify conditions for the calculation of data. Not just calculations you can also count the chars in cells, add date, day, or time, and even pick random data. 

How to insert an Array Formula?

Before entering the Array formula fir of all we understand some important points about the Array formula:

• After typing the formula you have to press keys CTRL+SHIFT+ENTER together. It will automatically change the normal formula into an array formula. 
• If you manually type braces around the formula then it will not convert the formula into an array formula. You have to use CTRL+SHIFT+ENTER keys to convert the formula into an array formula.
• Whenever you edit the array formula the braces will disappear automatically and you have to again press the combination of CTRL+SHIFT+ENTER keys.
• If you forget to press the CTRL+SHIFT+ENTER keys then your formula will work as the normal formula.

Now let’s understand inserting an array formula.

Single Cell Array formula

Every array formula returns the result in either single or in multiple cells. So when an array formula returns its result in the single-cell then such type of formula is known as a single-cell array formula. Such types of formulas are SUM, AVERAGE, AGGREGATE, MAX, MIN, etc. Follow the following steps to use the single-cell array formula:

Step 1: Select the cell where you want to store the answer.

Step 2: Now go to the formula bar and write an “=” sign.

Step 3: Now to formulas (highlighted below), and select the operation you want to perform.

Step 4: Here we want to perform the sum operation. Click on sum and a new popup will open. Write the cells you want to perform the operation with.

Multi-Cell Array Formula

If you wish to perform the same calculation with more cells then you can use the multi-cell formula. You can implement it in two ways. Functions like TRANSPOSE, TREND, FREQUENCY, LINEST, etc are used for the multi-cell arrays. Implement the formula in single-cell by following the above steps. Now, drag the selection up to the cells you want to implement the formula. Below is the implementation of doing that.

Alternatively,

Specify the range of cells and an operator between them. For example, =(B1:B7 + C2:C7) and press Ctrl+Shift+Enter. 

Excel Array Constants

Excel array contacts are a set of static values and can’t be changed. These values remain constant regardless of the operations performed on them. Now we will see how to create Array Constants in Excel and will perform different actions on them. There are three types of array constant available:

1. Horizontal or Row Array constant

A horizontal constant is present in a row. To create a horizontal constant we have to type multiple values separated by a comma in the enclosed braces. To enter a row array follow these steps below:

Step 1: Select the cells you want to work with.

Step 2: Go to the formula bar and start with an equal sign. 

Step 3: Now enter the array you want to create in braces {}, separated by commas(,). Ex:- ={1,2,3,4,5}

Step 4: Now press Ctrl+Shift+Enter.

2. Vertical or Column Array

Vertical array constants are generally present in Column Array. To create a vertical constant we have to type multiple values separated by a semicolon in the enclosed braces. To enter a column array follow these steps below:

Step 1: Select the cells you want to work with.

step 2: Go to the formula bar and start with an equal sign. 

Step 3: Now enter the array you want to create in braces {} separated with termination sign(;). Ex:- ={“Coding”;”GFG”;”GeeksforGeeks”}

Step 4: Now press Ctrl+Shift+Enter.

3. 2-D array

In Excel, you are allowed to create a 2-D array. So to create a 2-D array constant, we have to type multiple values in which rows are separated by semicolons and d columns are separated by commas. Let’s understand the implementation of a 2-d array. 

Step 1: Select the cells you want to work with.

Step 2: Go to the formula bar and start with an equal sign. 

Step 3: Now enter the array you want to create in braces {} separated with commas(,) for entering the values in same row, termination sign(;) for row change. Ex:- ={1,2,3;”Coding”,”GFG”,”GeeksforGeeks”}

Step 4: Now press Ctrl+Shift+Enter.

Working with Constant arrays

In the Excel formula, array constants are the important part. Some of the important concepts of Array constant are:

1. Elements: To create elements of array constant we have to follow the following points:

1. The elements of an array constant must be of numeric, alphabetic, boolean, or scientific notation and each of them is separated by commas or semicolons.
2. The elements of an array constant do not contain an array, cell reference, dates functions formulas, defined names, etc.
3. You can also be allowed to use text in the array of the element but the text is surrounded by hyphens(“”). 

2. Naming Array Constants: You can name any array and use them as a variable for further references. For naming an array, follow the steps below:

1. Go to the formula tab. and select Define Name.
2. Write the array name in the name. You can also add some comments related to your array.
3. Click on OK.

3. Common Errors: Following are the common errors that will happen while working with array constants:

1. The use of delimiters in between the elements.
2. The selection of range is also an important point to remember. 

Unary Operator in Excel Array Formulas

Using unary operators we can process the array using AND and OR operators. 

1. AND: It is denoted by an asterisk(*) symbol. It returns true if and only if all conditions are true, 
2. OR: It is denoted by a plus(+) symbol. It returns true if any of the statement is true.

These operators are more useful when you have the same variable with a different value. For example, let’s consider a case, where data of 3 sellers of different months are given and you have to how much Shyam sold potatoes.

Excel worksheet arrays and vectors

This material about arrays and vectors involves three concepts:

1. Excel structures able to hold data, most commonly, the array of cells on a worksheet (by reference, name or constant)
2. mathematical element wise array operations, and
3. matrix based linear algebra array operations

An array can be described as a group of items that can be acted on either individually or collectively. An array’s orientation is classified by its dimension (such as column orientation, or row orientation, discussed further in section 1). In Excel the concept is best illustrated by example, see figure 1 (worksheet: WS arrays) where «a group of items» means a contiguous range, In particular, an array can be a:

• Scalar — a single cell
• Column array (column vector) — range B2:B7 shaded green
• Row array (row vector) — range B9:E9 shaded blue
• Multi dimensional array — range B11:D14 shaded grey

The expressions «scalar», «row vector» and «column vector» are common to the MatLab (matrix laboratory) application software.

1. Arrays — concepts

Dimension

The size of an array is described by the number of rows and number of columns. By convention the dimension is always rows first and columns second, in the spirit of R1C1 reference style, and the ordering of row and column arguments in functions such as INDEX and OFFSET.

Excel uses [mR x nR] during selection resizing operations (m and n are common to MatLab). MatLab uses m x n notation, with m being the number of rows (first dimension) and n being the number of columns (second dimension). Thus [2R x 3C] is a 2 row by 3 column array.

An array is contiguous, meaning rectangular / square, and a worksheet array can be referenced by the top left cell and bottom right cell with the range operator, see B11:DF14 in figure 1. Some functions return an array (eg. the TRANSPOSE and MMULT functions).

Dimensions (from figure 1):

• Scalar: dimension 1 x 1 (not shown in figure)
• Column vector: named ColArr, dimension 6 x 1, number of elements 6
• Row vector: named RowArr, dimension 1 x 4, number of elements 4
• MultiDimensional array: a two dimensional array named MDArr, dimension 4 x 3, number of elements 12

In mathematics, the arrays in figure 1 can presented in the form:

$$text{ColArr}=begin{bmatrix} r1 \ r2 \ r3 \ r4 \ r5 \ r6 end{bmatrix},
qquad text{RowArr}=begin{bmatrix} c1 & c2 & c3 & c4 end{bmatrix}
qquad text{MDArr}=begin{bmatrix} r1c1 & r1c2 & r1c3 \ r2c1 & r2c2 & r2c3 \ r3c1 & r3c2 & r3c3 \ r4c1 & r4c2 & r4c3 end{bmatrix}$$

where [ ] represents the array.

Name Manager curly braces «{}»

In Excel there are two representations of arrays:

1. the worksheet depiction in figure 1, and
2. computer memory depictions such as the Value and Refers To field of the Name Manager (figure 2)

Value field

The three arrays from figure 1 are stored arrays link and are labeled in figure 2

• Excel arrays use opening «{» and closing «}» curly braces
• Arrays are constructed on a row by row basis
• Individual elements are separated by a comma «,»
• End of row is marked by a semi-colon «;» except for the last row
• These formats do not apply to a scalar

In Excel array notation:

1. Name: ColArr; Value: {"r1";"r2";"r3";"r4";"r5";"r6"}
2. Name: RowArr; Value: {"c1","c2","c3","c4"}
3. Name: MDArr; Value: {"r1c1","r1c2","r1c3";"r2c1","r2c2","r2c3";"r3c1","r3c2","r3c3";"r4c1","r4c2","r4c3"}

«Refers To» field

The array ArrConst, labeled in figure 2 is a named array constant. It has 2 x 2 dimension and is used in the Named Array Const worksheet in figure 3.

In Excel array notation, the named array constant has:

1. Name: ArrConst;
2. Value: {...} curly braces with a horizontal ellipses;
3. Refers To: {"A",1;"XFD",1048576}

To enter the array, select a 2 x 2 range, type =ArrConst in the Formula Bar, then press Control + Shift + Enter to complete the formula.

A named array constant

• can contain numbers, text, logical values (TRUE and FALSE) and error values (like #N/A!)
• all text must be in double quotes «»
• cannot contain other arrays, formulas, or functions
• percentages must be decimal or text (0.10 or «10%»)

Function Arguments curly braces «{}»

Array values are displayed in the Function Arguments dialog box to the right of the argument name (figure 4). A maximum of 36 characters are shown.

Formula F2 F9 curly braces «{}»

You can check the values in an array (or reference) with the F2 F9 sequence. In figure 5, the cell F2 has the formula =COUNTA(ColArr). To check the values in the array

1. switch to Edit mode by pressing F2
2. select the reference ColArr in the Formula Bar
3. press F9 to debug part of a formula. The result is displayed in the figure
4. this technique is limited by the formula maximum of 8,192 characters (2 ^ 13)

2. Arrays — element wise operators

Operations on an array, as described in section 2, requires an array formula which has several distinct features compared to a conventional formula in Excel.

• An array formula is completed by pressing the CONTROL + SHIFT + ENTER key sequence often referred to by the abbreviation CSE formula
• There two distinct types of operations involving arrays
  1. Element by element, and
  2. Matrix (based on linear algebra)
• Only element by element is covered in this module
• (Generally) Each array must have the same magnitude and direction. In other words, the name dimension (excluding 1 x 1 scalar arrays)
• You cannot edit or delete part of an array. You must select the current array — use the Ctrl + / shortcut, or

Example — Excel Online #1

From the «element wise» worksheet in figure 6. The example uses two row vectors each of dimension (1 x 3). The range names of the arrays and values are: x = [1,2,3], and y = [4,5,6], and they appear in rows 4 and 5 of figure 6

WS1: the element wise worksheet demonstrates:

1. Addition
2. Subtraction
3. Multiplication
4. Division
5. Scalar addition
6. Scalar subtraction
7. Scalar multiplication
8. Scalar division
9. Scalar exponentiation
10. Scalar logical

WS2: The U x P >> Sales worksheet demonstrates a small data base of Unit number and Price data, the user is required to:

1. Calculate Total Sales using normal cell formulae and the SUM function
2. Calculate Total Sales using CSE formulae for sales then SUM
3. Calculate Total Sales using CSE formulae in the final cell
4. Repeat step 3 using the Excel SUMPRODUCT function

Each vector is 6 x 1.

WS3: The 100 records no IF filter worksheet uses the 100 records data base to demonstrate vector logical CSE formulas. Required:

1. Sum product A, B and C for Salesperson = "Wong"
2. Sum product A, B and C for Salesperson = "Wong" AND Month = "September"
3. Sum product A for Salesperson = "Wong" AND Product A >= 10 AND Product A <= 30

Each field column uses the label as vector name. For example, the Invoice No field has vector name Invoice_No

The CSE formulas are (in Ready mode):

1. {=SUM((Salesperson = "Wong") * Prod_C_qty)}
2. {=SUM((Salesperson="Wong") * (Month="September") * Prod_C_qty)}
3. {=SUM((Salesperson="Wong") * (Prod_A_qty >= 10) * (Prod_A_qty <= 30) * Prod_A_qty)}

WS4: The NPV as CSE worksheet uses using the VisiCalc handbook numbers, and the xlf Carrot Washer example.

The technique is a direct interpretation of the NPV equation —
$$begin{equation} NPV=sum_{t=0}^{n} frac{C_t}{(1+k)^t} end{equation}$$ where the initial cash flow at time zero and future cash flows at time (t) are denoted (C_t) over (n) periods. (k) is the periodic discount rate.

Using equation 1, the application is:

The VisiCalc example
$$ NPV=frac{-20,000}{(1+0.1)^{0}} + frac{3,000}{(1+0.1)^{1}} + frac{7,500}{(1+0.1)^{2}}+ frac{15,000}{(1+0.1)^{3}}+ frac{25,000}{(1+0.1)^{4}}+ frac{30,000}{(1+0.1)^{5}} = $35,898 $$

The carrot washer example
$$ NPV=frac{-80,000}{(1+0.05)^{0}} + frac{10,000}{(1+0.05)^{1}} + frac{20,000}{(1+0.05)^{2}}+ frac{15,000}{(1+0.05)^{3}}+ frac{50,000}{(1+0.05)^{4}}+ frac{20,000}{(1+0.05)^{5}} = $17,428 $$

The CSE formulas for the NPV estimates are:

1. VisiCalc =SUM(Cashflows / (1 + Disc) ^ {0;1;2;3;4;5}) returns 35,898.32, where {0;1;2;3;4;5} is an array constant (column orientation 6 by 1)
2. carrot washer =SUM(Cashflows2 / (1 + Disc2) ^ (ROW(1:6) - 1)) returns 17,427.61

• Development platform: Excel 2016 (64 bit) Office 365 ProPlus on Windows 10
• Related material: Add a series of relative offset names to the Name Manager
• O’Connor I, (2015) Convert lower triangle table to full matrix. Includes discussion of array / matrix dimension and element indexing
• O’Connor I, (2017) Excel functions with array arguments. Includes array (CSE) and enter formulas
• O’Connor I, (2015) Vector to array constant. Includes VBA code for text based vector
• Revised: Saturday 25th of February 2023 — 10:12 AM, [Australian Eastern Time (AET)]

Author: Oscar Cronquist Article last updated on February 10, 2023

This article explains the basics of array formulas, read this article if you never have used array formulas before. It opened up a new world to me and I am sure you will find many applications for these kinds of calculations.

1. Why are array formulas so powerful?

They allow you to do things not possible with regular formulas, an array formula can do multiple calculations based on several values simultaneously. You can do some seriously complicated calculations, Excel is definitively a powerful tool.

The array formula example, demonstrated in the image above, performs calculations to multiple numbers simultaneously and returns the smallest number from those calculations.

It multiplies all numbers in column B with all numbers in column D and returns the smallest product of all numbers.

Array formula in cell D9:

=MIN(B3:B7*TRANSPOSE(D3:D6))

Explaining formula in cell D9

Step 1 — Transpose numbers

It is not possible to multiply two vertical arrays containing a different amount of numbers. The TRANSPOSE function converts a vertical array to horizontal and vice versa.

However, if they were of identical size the result would not be what we are looking for anyway, the first number would be multiplied with the first value in the second array only. We want each value multipled with all numbers in the second array to calculate all combinations.

TRANSPOSE(D3:D6)

becomes

TRANSPOSE({1.4;5.2;4.2;0.7})

and returns {1.4,5.2,4.2,0.7}.

Note that the delimiting character is a semicolon in the vertical array and a comma in the horizontal array.

The image above shows the numbers in the second array arranged horizontally.

Step 2 — Multiply numbers

B3:B7*TRANSPOSE(D3:D6)

becomes

B3:B7*{1.4,5.2,4.2,0.7}

becomes

{4;3;6;0.5;5}*{1.4,5.2,4.2,0.7}

and returns {5.6,20.8,16.8,2.8;4.2,15.6,12.6,2.1;8.4,31.2,25.2,4.2;0.7,2.6,2.1,0.35;7,26,21,3.5}.

The result is shown in cell range H3:K7 in the image above. Cell H3 shows the product of the numbers in cell H2 and G3, and so on.

Step 3 — Extract the smallest number in the array

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

MIN(B3:B7*TRANSPOSE(D3:D6))

becomes

MIN({5.6,20.8,16.8,2.8;4.2,15.6,12.6,2.1;8.4,31.2,25.2,4.2;0.7,2.6,2.1,0.35;7,26,21,3.5})

and returns 0.35 which is the smallest number in the array.

The image below shows the result in cell D9, all these calculations were completed in one cell only.

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2. How to identify array formulas?

The formula bar is above your worksheet, it may be empty or contain a value or a formula. The image above demonstrates an array formula in cell D9.

The formula bar shows what kind of formula the selected cell contains. An array formula begins with a curly bracket and ends with a curly bracket.

These curly brackets appear automatically if you enter the formula as an array formula, see next section below on how to do that.

3. How to enter an array formula?

Constructing an array in Excel is easy. Double press with left mouse button on cell A1 and type ={1,2,3} in the formula bar and hold and press CTRL + SHIFT simultaneously, then press Enter once. Release all keys.

The formula in the formula bar now shows a beginning and ending curly bracket. Don’t enter those characters yourself. Make sure the formula bar looks like this: {={1,2,3}}

If your formula bar looks like the picture above then you have made your first array! If not try again.

={1,2,3} is an array of constants separated by a delimiting character. This formula is entered in cell A1 but only one value in the array is displayed, why is that? The next section below explains why this happens.

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4. Why is only one value shown? I have x values in the array?

There can only be one value in each cell. To be able to see all values enter the formula in cell range A1:C1

1. Select cell range A1:C1
2. Press with left mouse button on in the formula bar
3. Press and hold CTRL + SHIFT simultaneously
4. Press Enter
5. Release all keys

The animated picture above shows you how to extend an array formula from cell A1 to A1:C1, this allows you to see all values in the array.

You have now extended the formula to three cells and all values in the array are visible on the sheet, see picture above.

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5. What are vertical and horizontal arrays?

You can construct arrays with a comma delimiter and a semicolon delimiter.

What is the difference? Use the comma when you want values horizontally and semicolon vertically. Look at the formula bar in this animated picture:

You can also combine colons and semicolons. ={1,2;3,4} A comma tells excel that the next value is to the right of the first value. A semicolon puts the next value on the next row.

I try to enter an array with text values but it doesn’t work, why? Use double quotes around your values, like this: ={«A»,»B»}

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6. How to use cell references in array formulas

All arrays presented above contain constants, meaning they don’t change unless you edit them. This formula =A1:A10 contains a cell reference to A1:A10. The values in this formula change if you change a value in cell range A1:A10. Formula =A1:A10 does not contain any constants.

This means that you can use values on your sheet in your array formula. This is extremely useful.

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7. How to quickly build an array

I want to construct an array from 1 to 1000? I don’t want to enter all these values.
You don’t have to, the ROW function can do that for you. =ROW(1:1000) creates an array from 1 to 1000.

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8. How to hard code (literal) values in array formulas?

Can I hard code values from 1 to 1000 in a formula without entering them myself? Yes, you can. Type =ROW(1:1000) in the formula bar and press F9.

Excel converts =ROW(1:1000) to ={1,2,3, … , 1000)

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9. Is Ctrl + Shift + Enter always necessary?

Can I build an array formula without entering it as an array formula?
Yes, you often can. However, it makes the formula more complicated.
Read this post:  No more array formulas?

Excel 365 users enter array formulas as regular formulas, I recommend upgrading to Excel 365. There are so many new things in Excel 365.

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10. Can I enter an array formula in merged cells?

Excel tells me «Array formulas are not valid in merged cells», how can I enter array formulas in merged cells?
Yes, you can enter array formulas in merged cells using a workaround: How to enter array formulas in merged cells however, I recommend that you avoid merged cells as much as possible.

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11. Are there any exceptions?

Yes, both the SUMPRODUCT function and the LOOKUP function lets you build arrays without requiring you to enter them as an array formula.

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The INDEX function lets you encapsulate an array so you don’t need to enter it as an array formula:

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12. Any caveats using array formulas?

A major disadvantage with array formulas is that if you double press with left mouse button on a cell containing an array formula and then press with left mouse button on another cell, the array formula changes to a regular formula. Beginner Excel users may not know about this and could possibly break your worksheet calculations.

However, this is not the case if you press the Escape key to exit editing an array formula or if you press CTRL + SHIFT + Enter.

Array formulas can slow down your worksheet calculations.

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13. Alright, show me some useful array formulas?

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Cool, even more complicated calculations?

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14. Excel 365 dynamic array formulas

You can enter array formulas in Excel 365, however, there is no need to do that. Microsoft has now changed how array formulas are entered, they are entered as a regular formula and are now called dynamic array formulas.

Excel 365 shows all values that the array formula returns automatically if the array formula returns more than one value, this behavior is called spilling.

The image above shows a dynamic array formula in cell H3 that returns multiple values and spills those values to cells below. The FILTER function is a new function only available for Excel 365 users.

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