The SMALL function returns the k-th smallest value from a group of numbers. The first argument is a cell range or array that you want to find the k-th smallest number in.
The second and last argument is k which is a number from 1 up to the number of values you have in the first argument.
Example shown in the above image, formula in cell E3 returns 17 because it is the third smallest number in cell range B3:B11.
=SMALL(B3:B11, D3)
Cell range B3:B1 contains the following numbers: 65, 50, 17, 22, 20, 66, 13, 18, and 15. Cell D3 contains the number that specifies which k-th smallest number to extract.
1. SMALL Function Syntax
SMALL(array, k)
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2. SMALL Function 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. |
The SMALL function is very versatile and is, in my opinion, one of the most used functions in Microsoft Excel. You can construct both regular and array formulas with the SMALL function.
It also ignores blank values and text values, however, not error values. This article explains a workaround if you have error values in your data set.
How to ignore error values using the SMALL function
You can use a cell range across multiple columns like:
=SMALL(B3:D14, 2)
It will also work with multiple non-adjacent cell ranges with minor changes to the formula.
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3. How does the SMALL function handle text and blank values?
The image above shows a formula in cell B13 that extracts the third smallest value from cell range B3:B10. Note that the cell range contains both text values and blank cells.
=SMALL(B3:B10, 3)
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.
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4. How to use constants (hardcoded) values in the SMALL function
In case you want to work with an array instead of a cell range in the SMALL function use curly brackets like this:
=SMALL({3, 5, 1}, 2)
This means that the values are hardcoded into the formula, however, you still enter it as a regular formula.
There is one downside with this approach and that is that you must edit the formula to be able to change a value in the array.
To convert a cell range to an array select the cell reference in the formula and press function key F9.
This will convert the cell range to an array of values.
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5. How to use a condition in the SMALL function
This array formula in cell F7 calculates the second smallest number from cell range C4:C14 based on a condition specified in cell F3.
=SMALL(IF(B4:B14=F3, C4:C14, ""), F4)
The IF function returns one value if the logical test returns TRUE and another value if the logical test is FALSE.
IF(logical_test, [value_if_true], [value_if_false])
In this case, the IF function compares the values in cell range B4:B14 to the value in cell F3 and returns and an array that contains boolean values TRUE or FALSE.
SMALL(IF(B4:B14=F3, C4:C14, ""), F4)
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)
The IF function then returns the corresponding value from the second argument if TRUE and the third argument if FALSE.
SMALL(IF({FALSE; TRUE; FALSE; TRUE; FALSE; FALSE; FALSE; TRUE; FALSE; FALSE; TRUE}, C4:C14, ""), F4)
becomes
SMALL(IF({FALSE; TRUE; FALSE; TRUE; FALSE; FALSE; FALSE; TRUE; FALSE; FALSE; TRUE},{55.47; 60.69; 5.83; 8.08; 94.68; 70.79; 41.03; 24.44; 81.68; 72.67; 2.25},""), F4)
becomes
SMALL({"";60.69;"";8.08;"";"";"";24.44;"";"";2.25}, 2)
and returns 8.08 in cell F7.
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6. How to quickly return sorted numbers using the SMALL function
Formula in cell E3:
=SMALL($B$3:$B$11, ROWS($A$1:A1))
The second argument k can be changed from a number to a function that returns numbers, this can be handy when you want to return multiple numbers sorted from small to large.
SMALL(array, k )
The ROWS function returns the number of rows a cell range contains. If you combine absolute and relative references into one cell reference you can build a dynamic cell reference that changes when you copy the cell and paste to cells below.
$A$1:A1
The first part of the cell reference is absolute meaning it won't change when the cell is copied and pasted to cells below. You can see that it is absolute bu the $ dollar signs in front of the column letter and the row number.
The colon is used to describe a cell range that contains multiple cells however it can also describe a reference to a single cell. The second part is relative meaning it will change when you copy the cell.
For example, the table below demonstrates how the cell references in the formula change when copied.
Cell E3: =SMALL($B$3:$B$11, ROWS($A$1:A1))
Cell E4: =SMALL($B$3:$B$11, ROWS($A$1:A2))
Cell E5: =SMALL($B$3:$B$11, ROWS($A$1:A3))
Note that you need to copy the cell not the formula to take advantage of growing cell references.
The cell range expands by one row for each new cell below you paste it to. The ROWS function calculates the number of rows in that cell range and returns that number.
Cell E3: =SMALL($B$3:$B$11, 1)
Cell E4: =SMALL($B$3:$B$11, 2)
Cell E5: =SMALL($B$3:$B$11, 3)
You can press and hold on the black dot in the bottom right corner of the selected cell then drag down as far as needed to quickly copy the cell to cells below, see animated image above.
You can also double press with left mouse button on with left mouse button on the black dot located in the bottom right corner of the selected cell to quickly copy the cell to cells below.
Excel uses existing values in the adjacent column to determine when to stop copying.
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'SMALL' function examples
Bill reminder in excelBrad asks: I'm trying to use your formulas to create my own bill reminder sheet. I envision a workbook where […]
Functions in this article
Functions in 'Statistical' category
The SMALL function function is one of many functions in the 'Statistical' category.
Calculates the average of the absolute deviations of data points from their mean.
Calculates the average of numbers in a cell range.
Returns the average of a group of values. Text and boolean value FALSE evaluates to 0. TRUE to 1.
Returns the average of cell values that are valid for a given condition.
Returns the average of cell values that evaluates to TRUE for multiple criteria.
Calculates the beta distribution.
Calculates the inverse of the cumulative beta distribution.
Calculates the individual term binomial distribution probability.
Calculates the minimum value for which the binomial distribution is equal to or greater than a given threshold value.
Calculates the probability of the chi-squared distribution, cumulative distribution or probability density.
Calculates the right-tailed probability of the chi-squared distribution.
Calculates the inverse of the left-tailed probability of the chi-squared distribution.
Calculates the inverse of the right-tailed probability of the chi-squared distribution.
Calculates the test for independence, the value returned from the chi-squared statistical distribution and the correct degrees of freedom. Use this function to check if hypothesized results are valid.
Calculates the confidence interval for a population mean.
Calculates the confidence range for a population mean using a Student's t distribution.
Calculates the correlation between two groups of numbers.
Counts all numerical values in an argument.
Counts the non-empty or non-blank cells in a cell range.
Counts empty or blank cells in a range.
Calculates the number of cells that is equal to a condition.
Calculates the number of cells across multiple ranges that equals all given conditions.
Calculates the covariance meaning the average of the products of deviations for each pair in two different datasets.
Calculates the sample covariance meaning the average of the products of deviations for each pair in two different datasets.
Calculates the exponential distribution representing an outcome in the form of probability.
Calculates the F probability for two tests.
Calculates the right-tailed F probability for two tests.
Calculates the two-tailed probability from an F-test
Calculates a value based on existing x and y values using linear regression.
Calculates how often values occur within a range of values and then returns a vertical array of numbers.
Calculates the GAMMA value.
Calculates the gamma often used in queuing analysis (probability statistics) that may have a skewed distribution.
Calculates the geometric mean.
Returns estimated exponential growth based on given data.
Calculates the harmonic mean.
Returns a value representing the y-value where a line intersects the y-axis.
Calculates the kurtosis.
Calculates the k-th largest value from an array of numbers.
Returns an array of values representing the parameters of a straight line based on the "least squares" method.
Returns an array of values representing the parameters of an exponential curve that fits your data, based on the "least squares" method.
Calculates the lognormal distribution of argument x, based on a normally distributed ln(x) with the arguments of mean and standard_dev.
Calculate the largest number in a cell range.
Calculates the highest value based on a condition or criteria.
Calculates the median based on a group of numbers. The median is the middle number of a group of numbers.
Returns the smallest number in a cell range.
Returns the smallest number. Text values and blanks are ignored, boolean value TRUE evaluates to 1 and FALSE to 0 (zero).
Calculates the smallest value based on a given set of criteria.
Returns the most frequent number in a cell range. It will return multiple numbers if they are equally frequent.
Calculates the most frequent value in an array or range of data.
Calculates the normal distribution for a given mean and standard deviation.
Calculates the inverse of the normal cumulative distribution for a given mean and standard deviation.
Calculates the percent rank of a given number in a data set.
Calculates the percent rank of a given number compared to the whole data set.
Returns the number of permutations for a set of elements that can be selected from a larger number of elements.
Returns the number of permutations for a specific number of elements that can be selected from a larger group of elements.
Calculates a number of the density function for a standard normal distribution.
Calculates the probability that values in a range are between a given lower and upper limit.
Returns the quartile of a data set.
Returns the quartile of a data set, based on percentile values from 0..1, inclusive.
Returns the rank of a number out of a list of numbers.
Calculates the rank of a number in a list of numbers, based on its position if the list were sorted.
Calculates the skewness of a group of values.
Calculates the slope of the linear regression line through coordinates.
Returns the k-th smallest value from a group of numbers.
Calculates a normalized value from a distribution characterized by mean and standard_dev.
Returns standard deviation based on the entire population.
Returns standard deviation based on a sample of the entire population.
Estimates the standard deviation from a sample of values.
Returns the standard deviation based on the entire population, including text and logical values.
Calculates values along a linear trend.
Calculates the mean of the interior of a data set.
Returns the variance based on the entire population. The function ignores logical and text values.
The VAR.S function tries to estimate the variance based on a sample of the population. The function ignores logical and text values.
Excel function categories
Excel functions that let you resize, combine, and shape arrays.
Functions for backward compatibility with earlier Excel versions. Compatibility functions are replaced with newer functions with improved accuracy. Use the new functions if compatibility isn't required.
Perform basic operations to a database-like structure.
Functions that let you perform calculations to Excel date and time values.
Let's you manipulate binary numbers, convert values between different numeral systems, and calculate imaginary numbers.
Calculate present value, interest, accumulated interest, principal, accumulated principal, depreciation, payment, price, growth, yield for securities, and other financial calculations.
Functions that let you get information from a cell, formatting, formula, worksheet, workbook, filepath, and other entitites.
Functions that let you return and manipulate logical values, and also control formula calculations based on logical expressions.
These functions let you sort, lookup, get external data like stock quotes, filter values based a condition or criteria, and get the relative position of a given value in a specific cell range. They also let you calculate row, column, and other properties of cell references.
You will find functions in this category that calculates random values, round numerical values, create sequential numbers, trigonometry, and more.
Calculate distributions, binomial distributions, exponential distribution, probabilities, variance, covariance, confidence interval, frequency, geometric mean, standard deviation, average, median, and other statistical metrics.
Functions that let you manipulate text values, substitute strings, find string in value, extract a substring in a string, convert characters to ANSI code among other functions.
Get data from the internet, extract data from an XML string and more.
Excel categories
Latest updated articles.
More than 300 Excel functions with detailed information including syntax, arguments, return values, and examples for most of the functions used in Excel formulas.
More than 1300 formulas organized in subcategories.
Excel Tables simplifies your work with data, adding or removing data, filtering, totals, sorting, enhance readability using cell formatting, cell references, formulas, and more.
Allows you to filter data based on selected value , a given text, or other criteria. It also lets you filter existing data or move filtered values to a new location.
Lets you control what a user can type into a cell. It allows you to specifiy conditions and show a custom message if entered data is not valid.
Lets the user work more efficiently by showing a list that the user can select a value from. This lets you control what is shown in the list and is faster than typing into a cell.
Lets you name one or more cells, this makes it easier to find cells using the Name box, read and understand formulas containing names instead of cell references.
The Excel Solver is a free add-in that uses objective cells, constraints based on formulas on a worksheet to perform what-if analysis and other decision problems like permutations and combinations.
An Excel feature that lets you visualize data in a graph.
Format cells or cell values based a condition or criteria, there a multiple built-in Conditional Formatting tools you can use or use a custom-made conditional formatting formula.
Lets you quickly summarize vast amounts of data in a very user-friendly way. This powerful Excel feature lets you then analyze, organize and categorize important data efficiently.
VBA stands for Visual Basic for Applications and is a computer programming language developed by Microsoft, it allows you to automate time-consuming tasks and create custom functions.
A program or subroutine built in VBA that anyone can create. Use the macro-recorder to quickly create your own VBA macros.
UDF stands for User Defined Functions and is custom built functions anyone can create.
A list of all published articles.
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 array
Yes 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. […]