## How to use the SMALL function

*Article last updated on May 04, 2018*

The SMALL function returns the k-th smallest value from a group of numbers.

Example, formula in cell E3 returns 5 because it is the third smallest number in cell range B3:B7. 2, 3, 5, 5 and 6.

### Excel Function Syntax

SMALL(*array*, *k*)

### Arguments

array |
Required. A group of numbers you want to extract the k-th smallest number from. |

k |
Required. k-th value, 1 returns the smallest number, 2 returns the second smallest number etc. |

### Example 1 - Cell range contains numbers, text and blanks

becomes

=SMALL({3; 6; "A"; 5; "X"; 0; 4; 4},3)

Text strings and blanks are overlooked. The array becomes

=SMALL({3; 6; ; 5; ; ; 4; 4},3)

and returns 4. 4 is the third smallest numerical value in the array.

### Example 2 - Use a condition (Array formula)

The following array formula looks for the second smallest value in column C if corresponding value in adjacent column D is 2012-Dec:

becomes

=SMALL(IF({"2013-Jan"; "2012-Dec"; "2013-Jan"; "2012-Dec"; "2012-Nov"; "2013-Jan"; "2013-Jan"; "2012-Dec"; "2013-Jan"; "2012-Nov"; "2012-Dec"}="2012-Dec", C4:C14, ""), F4)

becomes

=SMALL(IF({FALSE;TRUE;FALSE;TRUE;FALSE;FALSE;FALSE;TRUE;FALSE;FALSE;TRUE}, C4:C14, ""), F4)

becomes

=SMALL({"";60.69;"";8.08;"";"";"";24.44;"";"";2.25}, 2)

and returns 8.08 in cell F7.

### Download excel *.xlsx file

### Articles with the 'SMALL' Function

The following 12 articles have formulas that contain the SMALL function.

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Extract largest values from two columns

Question: How do I extract the five largest values from two or more columns? Answer: Formula in A12: =INDEX(tbl, SMALL(IF(LARGE(tbl,ROW(A1))=tbl, […]

SMALL function – multiple criteria

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INDEX MATCH – multiple results

The array formula in cell E6 extracts values from column C when the corresponding value in column B matches the […]

SMALL function with duplicates

The formulas in column E, shown in the picture above, extracts the k-th smallest value from B3:B9 ignoring the duplicate numbers. […]

### Functions in 'Statistical'

The SMALL function function is one of many functions in the 'Statistical' category.

How to use the AVEDEV function

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How to use the AVERAGE function

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How to use the AVERAGEA function

The AVERAGEA function returns the average of a group of values. Text and boolean value FALSE evaluates to 0. TRUE to […]

How to use the AVERAGEIF function

The AVERAGEIF function returns the average of cell values that are valid for a given condition. Formula in cell D3: […]

How to use the AVERAGEIFS function

The AVERAGEIFS function returns the average of cell values that evaluates to TRUE for multiple criteria. Formula in cell F6: =AVERAGEIFS(D3:D8,B3:B8,F3,C3:C8,G3) […]

How to use the CORREL function

The CORREL function calculates the correlation between two groups of numbers. Formula in cell B12: =CORREL(C3:C9, D3:D9) The value in cell […]

The COUNT function counts all numerical values in an argument, it allows you to have up to 255 arguments. Blank […]

How to use the COUNTA function

The COUNTA function counts the non-empty or blank cells in a cell reference. The picture above demonstrates the COUNTA function […]

How to use the COUNTBLANK function

The COUNTBLANK function counts empty or blank cells in a range. The picture above demonstrates the COUNTBLANK function entered in […]

How to use the COUNTIF function

Counts the number of cells that meet a specific condition.

How to use the COUNTIFS function

Checks multiple conditions against the same number of cell ranges and counts how many times all criteria are met.

How to use the EXPON.DIST function

The EXPON.DIST function returns the exponential distribution. Use EXPON.DIST to model the time between events. Formula in cell C3: =EXPON.DIST(B3,C3,D3) […]

How to use the FORECAST.LINEAR function

The FORECAST.LINEAR function calculates a value based on existing x and y values using linear regression. Use this function to […]

How to use the FREQUENCY function

Returns how many times values exist in a given range. Note, this function returns an array of values.

The LARGE function calculates the k-th largest value from an array of numbers. Use the LARGE function, for example, to extract […]

The MAX function allows you to calculate the largest number in a cell range. The formula in cell D3 extracts […]

How to use the MAXIFS function

The MAXIFS function allows you to calculate the highest value based on a condition or criteria. Formula in cell G4: […]

How to use the MEDIAN function

The MEDIAN function calculates the median based on a group of numbers. The median is the middle number of a […]

The MIN function allows you to retrieve the smallest number in a cell range. The formula in cell D3 extracts […]

The MINA function returns the smallest number. Text values and blanks are ignored, boolean value TRUE evaluates to 1 and FALSE […]

How to use the MINIFS function

The MINIFS function calculates the smallest value based on a given set of criteria. Formula in cell E3: =MINIFS(C3:C10,B3:B10,"A") The […]

How to use the MODEMULT function

The MODE.MULT function calculates the most frequent number in a cell range. It will return multiple numbers if they are equally […]

How to use the NORM.DIST function

The NORM.DIST function calculates the normal distribution for a given mean and standard deviation. Formula in cell C7: =NORM.DIST(C2,C3,C4,C5) Excel […]

How to use the NORM.INV function

The NORM.INV function calculates the inverse of the normal cumulative distribution for a given mean and standard deviation. Formula in […]

How to use the PERMUT function

The PERMUT function returns the number of permutations for a set of elements that can be selected from a larger […]

How to use the PERMUTATIONA function

The PERMUTATIONA function returns the number of permutations for a specific number of elements that can be selected from a […]

The PHI function calculates a number of the density function for a standard normal distribution. Formula in cell C3: =PHI(B3) Excel […]

How to use the QUARTILE.INC function

The QUARTILE.INC function returns the quartile of a data set, based on percentile values from 0..1, inclusive. Use the Quartiles.inc […]

How to use the RANK.AVG function

The RANK.AVG function returns the rank of a number in a list of numbers. The number returned indicates its size […]

The SMALL function lets you extract a number in a cell range based on how small it is compared to the other numbers in the group.

How to use the STANDARDIZE function

The STANDARDIZE function calculates a normalized value from a distribution characterized by mean and standard_dev. Formula in cell C5: =STANDARDIZE(C2, […]

How to use the STDEV.P function

The STDEV.P function returns standard deviation based on the entire population. The standard deviation is how widely numbers are distributed […]

How to use the STDEV.S function

The STDEV.S function returns standard deviation based on a sample of the entire population. The standard deviation is how widely […]

How to use the STDEVA function

The STDEVA function estimates the standard deviation from a sample of values. Standard deviation shows how much the values differ […]

How to use the STDEVPA function

The STDEVPA function returns the standard deviation based on the entire population, including text and logical values. The standard deviation […]

The TREND function calculates values along a linear trend. Fits a straight line (using the method of least squares) to […]

How to use the TRIMMEAN function

The TRIMMEAN function calculates the mean of the interior of a data set. The function excludes a percentage of data […]

The VAR.P function returns the variance based on the entire population. The function ignores logical and text values. Variance shows […]

The VAR.S function tries to estimate the variance based on a sample of the population. The function ignores logical and […]

### 12 Responses to “How to use the SMALL function”

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Hi Oscar,

I am in love with.. your formula explanation.. :)

Waiting eagerly for MMULT & some D-Functions..

Regards,

Deb

Debraj Roy,

Thank you!

I am curious, in what situation do you use MMULT?

Hi Oscar,

We can use MMULT in all cases where SUMPRODUCT fails..

with only Two Criteria..

* Only TWO Array can be multiplied..

* 1st Array's No Of Row.. Should be Same as 2nd Array's No Of Column..

Unlike SUMPRODUCT, It returns ARRAY output..

I think, Binary Addition & Binary Multiplication are the base of all FORMULA's & FUNCTION..

and you are doing a great job, by teaching/using them in your daily blog..

Regards!

Deb

Debraj Roy,

Well, I am learning from you right now.

Can you provide an example where SUMPRODUCT fails and MMULT succeeds?

I searched and found my old mathematics books from college, I had forgotten the basics of multiplying two matrices. :-)

It is worthwhile mentioning that in both Small and Large K could also be an array

So if A1:A10 contains random numbers the below formulas

=Large(A1:A10,{1,2,3}) - Return an array containing the top 3 numbers

=SUM(Large(A1:A10,{1,2,3}) -Array entered Returns the Sum of the top 3 numbers

=SUM(LARGE(A1:A10,ROW(INDIRECT("1:"&TopN))))- Array Entered Returns the sum of the Top N numbers as defined in the Cell/Named Constant TopN

=Large(A1:A10,Row(A1:A10))- Array entered returns an array of numbers in A1:A10 in Descending order

Likewise Small

sam,

It is worthwhile mentioning that in both Small and Large K could also be an arrayYes you are right! Thanks for pointing that out.

[…] SMALL(array,k) Returns the k-th smallest number in this data set. […]

=Small({VALUE(DV147),VALUE(DZ147),VALUE(ED147),VALUE(EH147)},2) will not work. If I use sum and the "Value(-----)" amounts, it works.

What am I doing wrong?

The numbers are stored as text in those cells for other reasons.

[…] LARGE function extracts the n-th largest number twice for every two cells. This allows us to return both the […]

I'm using the SMALL function inside an array. I understand how to use the function to return an array where values are greater than or equal to a number. But how do I use the function if I want to return results that are between two numbers?

I've tried nesting an AND statement within the IF statement, but it isn't working (no values are returned).

Any suggestions? Thanks!

julie,

=SMALL(IF(($A$2:$A$10< $F$2)*($A$2:$A$10>$F$3),$A$2:$A$10,""),ROW(A1))

[…] LARGE(array,k) returns the k-th largest row number in this data set. […]