sorts the elements of list in the order defined by applying f to each of them.


breaks ties by successively using the values obtained from the fi.


sorts the elements of list using the function p to compare the results of applying f to each element.


represents an operator form of SortBy that can be applied to an expression.


  • SortBy[{e1,e2,e3,},f] sorts the ei so that the f[ei] lie in canonical order.
  • If some of the f[ei] are the same, then the canonical order of the corresponding ei is used.
  • SortBy[{e1,e2,e3,},f,p] sorts the ei so that the f[ei] are sorted according to the ordering function p: ei will be sorted before ej if p[f[ei],f[ej]] is 1 or True.
  • SortBy uses the canonical ordering described in the notes for Sort.
  • SortBy can be used on expressions with any head, not only List.
  • SortBy[f][list] is equivalent to SortBy[list,f].


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Basic Examples  (4)

Sort a list of lists by the last element of each sublist:

Sort by the total of each sublist:

Sort a list of integers by their values modulo 3:

Sort elements of an Association by their values modulo 3:

Use SortBy as an operator form:

Scope  (7)

Sort by numerical value:

The default order ranks these symbolically:

Sort by absolute numerical value:

Slightly faster way:

Sort by Re, Im, Arg, and Abs:

Sort by date:

Sort a list of vectors by their norm:

Their norms are sorted following canonical order, but not numerical order:

Explicitly request sorting of norms by numerical order:

Sort complex numbers by their modulus using numerical order:

Using canonical order gives a different result:

Sort by string length:

Sort according to decreasing lengths:

Generalizations & Extensions  (1)

SortBy can be used on expressions with any head:

Applications  (3)

Show the top 10 countries according to different criteria:

Sort the first 10 countries in alphabetical order by population:

Sort the first 10 countries in alphabetical order by area:

Sort mathematically equivalent expressions by different criteria:

Sort by LeafCount:

Sort by size of error for numerical evaluation with machine numbers at :

Take a subset of the passengers of the Titanic:

Sort by gender and then age:

Properties & Relations  (3)

SortBy[e,f] is equivalent to Sort[{f[#],#}&/@e][[All,-1]]:

ReverseSortBy uses reverse canonical ordering:

The result of ReverseSortBy[list,fs] is not always Reverse[SortBy[list,fs]]:

SortBy[list,f] is equivalent to list[[OrderingBy[list,f]]]:

Introduced in 2007
Updated in 2014