The Excel SMALL Function

Function Description

The Excel Small function returns the k'th smallest value from an array of numeric values.

The syntax of the function is:

SMALL( array, k )

where the function arguments are:

 array - An array of numeric values from which you want to find the k'th smallest value. k - The index (i.e. the function returns the k'th smallest value from the supplied array).

The array argument can be supplied to the function either directly, or as a reference to a range of cells containing numeric values. If values in the supplied range of cells are text values, these values are ignored.

Small Function Examples

The following spreadsheet shows the Excel Small function, used to retrieve the 1st, 2nd, 3rd, 4th and 5th smallest values from the set of values in cells A1-A5.

Formulas:
AB
16=SMALL( A1:A5, 1 )
212=SMALL( A1:A5, 2 )
315=SMALL( A1:A5, 3 )
41=SMALL( A1:A5, 4 )
54=SMALL( A1:A5, 5 )
Results:
AB
161
2124
3156
4112
5415

Note that in the above example spreadsheet:

• In cell B1, where k is set to 1, the Small function performs the same action as the Excel Min function;
• In cell B5, when k is set to 5 (the number of values in the supplied array), the Small function performs the same action as the Excel Max function.

Further details and examples of the Excel Small function are provided on the Microsoft Office website.

Small Function Errors

If you get an error from the Excel Small Function, this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if either:The supplied value of k is less than 1 or greater than the number of values in the supplied arrayorThe supplied array is empty. #VALUE! - Occurs if the supplied k is non-numeric.

Also, the following problem is encountered by some users:

Common Problem

The Small function returns the wrong value, or returns the #NUM! error, even though the supplied value of k is between 1 and the number of values in the supplied array.

Possible Reason

Text values, including text representations of numbers within the supplied array, are ignored by the Small function. Therefore, this problem may arise if the values in the supplied array are text representations of numbers, instead of actual values.

Solution

This problem can be solved by converting all array values into numeric values. For details of how to do this, see the Convert Text to Number page.