Statistical

SMALL Formula

SMALL returns the k-th smallest value from a data set. It is the inverse of LARGE — use it to find the lowest values, like the cheapest option, shortest delivery time, or the bottom performers in a ranked list.

Syntax

SMALL(array, k)
ParameterDescription
array Parameter of the SMALL function.
k Parameter of the SMALL function.
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Examples

Cheapest supplier quote

Formula
=SMALL(C2:C20, 1)
Returns the lowest quote from 19 suppliers. Equivalent to MIN(C2:C20) when k=1.

3rd fastest delivery

Formula
=SMALL(E2:E100, 3)
Returns the 3rd shortest delivery time in days. Useful for finding a realistic fast-delivery benchmark excluding the top 2 outliers.

Bottom 5 scores

Formula
=SMALL(B2:B500, ROW(A1:A5))
Returns the 5 lowest scores when entered as an array formula, useful for identifying students or employees who need the most help.

Common Errors

#NUM!

Returned if k is larger than the number of data points or less than 1. For 10 values, k must be between 1 and 10.

#VALUE!

Occurs when k is non-numeric.

Tips

SMALL(array, 1) equals MIN

For the absolute minimum, MIN and SMALL with k=1 are identical. SMALL is useful when you want the 2nd, 3rd, or n-th smallest.

Exclude zeros

To find the smallest non-zero value, use an array formula like =SMALL(IF(A1:A100>0, A1:A100), 1) to filter out zeros first.

Pair with LARGE for trimmed ranges

Use SMALL and LARGE together to exclude outliers: average everything between SMALL(data,3) and LARGE(data,3) to trim the top and bottom 2 values.

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