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Map
  • See Also
    • Apply
    • Scan
    • MapAll
    • MapAt
    • MapIndexed
    • MapApply
    • MapThread
    • SubsetMap
    • AssociationMap
    • KeyMap
    • KeyValueMap
    • ParallelMap
    • Level
    • Operate
    • Comap
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  • Related Guides
    • Applying Functions to Lists
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    • Wolfram Language Syntax
    • Expressions
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    • Associations
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    • Handling Arrays of Data
    • Language Overview
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  • Tech Notes
    • Applying Functions to Parts of Expressions
    • See Also
      • Apply
      • Scan
      • MapAll
      • MapAt
      • MapIndexed
      • MapApply
      • MapThread
      • SubsetMap
      • AssociationMap
      • KeyMap
      • KeyValueMap
      • ParallelMap
      • Level
      • Operate
      • Comap
      • Through
      • Thread
      • ImageApply
    • Related Guides
      • Applying Functions to Lists
      • Parts of Matrices
      • List Manipulation
      • Functional Programming
      • Wolfram Language Syntax
      • Expressions
      • Parts of Expressions
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      • Applying Functions to Parts of Expressions

Map[f,expr] or f/@expr

applies f to each element on the first level in expr.

Map[f,expr,levelspec]

applies f to parts of expr specified by levelspec.

Map[f]

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

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Level Specifications  
Types of Expressions  
Options  
Heads  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • Apply
    • Scan
    • MapAll
    • MapAt
    • MapIndexed
    • MapApply
    • MapThread
    • SubsetMap
    • AssociationMap
    • KeyMap
    • KeyValueMap
    • ParallelMap
    • Level
    • Operate
    • Comap
    • Through
    • Thread
    • ImageApply
  • Related Guides
    • Applying Functions to Lists
    • Parts of Matrices
    • List Manipulation
    • Functional Programming
    • Wolfram Language Syntax
    • Expressions
    • Parts of Expressions
    • Associations
    • Function Composition & Operator Forms
    • Looping Constructs
    • Handling Arrays of Data
    • Language Overview
    • Incrementals
  • Tech Notes
    • Applying Functions to Parts of Expressions
    • See Also
      • Apply
      • Scan
      • MapAll
      • MapAt
      • MapIndexed
      • MapApply
      • MapThread
      • SubsetMap
      • AssociationMap
      • KeyMap
      • KeyValueMap
      • ParallelMap
      • Level
      • Operate
      • Comap
      • Through
      • Thread
      • ImageApply
    • Related Guides
      • Applying Functions to Lists
      • Parts of Matrices
      • List Manipulation
      • Functional Programming
      • Wolfram Language Syntax
      • Expressions
      • Parts of Expressions
      • Associations
      • Function Composition & Operator Forms
      • Looping Constructs
      • Handling Arrays of Data
      • Language Overview
      • Incrementals
    • Tech Notes
      • Applying Functions to Parts of Expressions

Map

Map[f,expr] or f/@expr

applies f to each element on the first level in expr.

Map[f,expr,levelspec]

applies f to parts of expr specified by levelspec.

Map[f]

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

Details and Options

  • Map uses standard level specifications:
  • nlevels 1 through n
    Infinitylevels 1 through Infinity
    {n}level n only
    {n1,n2}levels n1 through n2
  • The default value for levelspec in Map is {1}.
  • A positive level n consists of all parts of expr specified by n indices.
  • A negative level -n consists of all parts of expr with depth n.
  • Level –1 consists of numbers, symbols, and other objects that do not have subparts.
  • Level 0 corresponds to the whole expression.
  • With the option setting Heads->True, Map includes heads of expressions and their parts.
  • Map always effectively constructs a complete new expression and then evaluates it.
  • If expr is an Association object, Map[f,expr] applies f to the values in the association. »
  • If expr is a SparseArray object or structured array, Map[f,expr] applies f to the values or subarrays that appear in expr. »
  • Map[f][expr] is equivalent to Map[f,expr].
  • Parallelize[Map[f,expr]] or ParallelMap[f,expr] computes Map[f,expr] in parallel on all subkernels. »

Examples

open all close all

Basic Examples  (5)

Evaluate f on each element of a list:

Wolfram Language code: Map[f, {a, b, c, d, e}]

Use the short input form:

Wolfram Language code: f /@ {a, b, c, d, e}

Use explicit pure functions:

Wolfram Language code: (1 + g[#])& /@ {a, b, c, d, e}
Wolfram Language code: Function[x, x ^ 2] /@ {1, 2, 3, 4}

Map at top level:

Wolfram Language code: Map[f, {{a, b}, {c, d, e}}]

Map at level 2:

Wolfram Language code: Map[f, {{a, b}, {c, d, e}}, {2}]

Map at levels 1 and 2:

Wolfram Language code: Map[f, {{a, b}, {c, d, e}}, 2]

Use a map operator:

Wolfram Language code: Map[f][{a, b, c, d}]

Map a function over values in Association:

Wolfram Language code: Map[h, <|a -> b, c -> d|>]

Scope  (11)

Level Specifications  (6)

Map at level 1 (default):

Wolfram Language code: Map[f, {{{{{a}}}}}]

Map down to level 2:

Wolfram Language code: Map[f, {{{{{a}}}}}, 2]

Map at level 2:

Wolfram Language code: Map[f, {{{{{a}}}}}, {2}]

Map on levels 0 through 2:

Wolfram Language code: Map[f, {{{{{a}}}}}, {0, 2}]

Map down to level 3:

Wolfram Language code: Map[f, {{{{{a}}}}}, 3]

Map on all levels, starting at level 1:

Wolfram Language code: Map[f, {{{{{a}}}}}, Infinity]

Map also at level 0:

Wolfram Language code: Map[f, {{{{{a}}}}}, {0, Infinity}]

Negative levels:

Wolfram Language code: Map[f, {{{{{a}}}}}, -1]
Wolfram Language code: Map[f, {{{{{a}}}}}, -2]
Wolfram Language code: Map[f, {{{{{a}}}}}, -3]

Positive and negative levels can be mixed:

Wolfram Language code: Map[f, {{{{{a}}}}}, {2, -3}]

Different heads at each level:

Wolfram Language code: Map[f, h0[h1[h2[h3[h4[a]]]]], {2, -3}]

Include heads in the levels specified:

Wolfram Language code: Map[f, {{{{a}}}}, 2, Heads -> True]

Types of Expressions  (5)

Map can be used on expressions with any head:

Wolfram Language code: Map[f, a + b + c + d]
Wolfram Language code: Map[f, x ^ 2 + y ^ 2, 2]

Map can be used on sparse arrays:

Wolfram Language code: SparseArray[{1 -> 1, 2 -> 2, 10 -> 10}]
Wolfram Language code: Map[f, %]
Wolfram Language code: Normal[%]

Use Map with structured arrays, such as SymmetrizedArray:

Wolfram Language code: SymmetrizedArray[{{1, 2} -> 1, {1, 3} -> 2, {2, 3} -> 3}, {3, 3}, Antisymmetric[All]]
Wolfram Language code: f /@ %

Use Map to apply a function to the elements of a structured array of type QuantityArray:

Wolfram Language code: QuantityArray[{{1, 2}, {3, 4}, {5, 6}}, "Meters"]
Wolfram Language code: Map[g, %, {2}]

Map at the second level of a nested Association:

Wolfram Language code: Map[h, <|a -> <|b -> c|>, d -> <|e -> f|>|>, {2}]

Map at several levels in an Association:

Wolfram Language code: Map[h, <|a -> <|b -> c|>, d -> {<|e -> f|>}|>, {1, 3}]

Options  (1)

Heads  (1)

By default, the function is not mapped onto the heads:

Wolfram Language code: Map[f, {a, b, c}]
Wolfram Language code: Map[f, {a, b, c}, Heads -> True]

Applications  (4)

Reverse all sublists:

Wolfram Language code: Reverse /@ {{a, b}, {c, d}, {e, f}}

Add the same vector to every vector in a list:

Wolfram Language code: Map[(# + {x, y})&, {{1, 1}, {2, 2}, {3, 3}, {4, 4}}]

Frame integers that are prime:

Wolfram Language code: If[PrimeQ[#], Framed[#], #]& /@ Range[20]

Supply additional constant arguments by using a pure function:

Wolfram Language code: Map[f[#, 3]&, {a, b, c}]

Properties & Relations  (9)

A function of several arguments can be mapped with MapThread:

Wolfram Language code: MapThread[f, {{1, 2, 3}, {a, b, c}}]

MapIndexed passes the index of an element to the mapped function:

Wolfram Language code: MapIndexed[f, {a, b, c}]

MapAll is equivalent to a specific level specification in Map:

Wolfram Language code: Map[f, {{a, b}, {c}, {{d}}}, {0, ∞}]
Wolfram Language code: MapAll[f, {{a, b}, {c}, {{d}}}]

Scan does the same as Map, but without returning a result:

Wolfram Language code: Map[Print, {a, b}]
Wolfram Language code: Scan[Print, {a, b}]

Functions with attribute Listable are mapped automatically:

Wolfram Language code: Attributes[Sqrt]
Wolfram Language code: Sqrt[{1, 2, 3, 4}]
Wolfram Language code: Map[Sqrt, {1, 2, 3, 4}]

ParallelMap computes Map in parallel:

Wolfram Language code: ParallelMap[PrimeQ[2 ^ # - 1]&, Range[100, 110]]

Map can be parallelized automatically, effectively using ParallelMap:

Wolfram Language code: Parallelize[Map[PrimeQ[2 ^ # - 1]&, Range[100, 110]]]

Map wraps an expression around parts of another expression:

Wolfram Language code: Map[f, {x, y, z}]

Comap wraps parts of an expression around another expression:

Wolfram Language code: Comap[{f, g, h}, x]

Map maps a function over the values in an association:

Wolfram Language code: Map[f, <|a -> 1, b -> 2, c -> 3|>]

KeyMap maps a function over the keys in an association:

Wolfram Language code: KeyMap[f, <|a -> 1, b -> 2, c -> 3|>]

KeyValueMap maps a function over the keys and values in an association (and returns a list):

Wolfram Language code: KeyValueMap[f, <|a -> 1, b -> 2, c -> 3|>]

AssociationMap maps a function over the rules in an association:

Wolfram Language code: AssociationMap[Reverse, <|a -> 1, b -> 2, c -> 3|>]

Map[f,assoc] is equivalent to AssociationThread[Keys[assoc]Map[f,Values[assoc]]]:

Wolfram Language code: assoc = <|1 -> a, 2 -> b, 3 -> c|>;
Wolfram Language code: Map[f, assoc] === AssociationThread[Keys[assoc] -> Map[f, Values[assoc]]]

Possible Issues  (1)

Map by default starts at level 1, so does not apply the function to the whole expression:

Wolfram Language code: Map[f, h1[h2[h3[x]]], -1]
Wolfram Language code: Map[f, h1[h2[h3[x]]], {0, -1}]

Neat Examples  (1)

Show nesting structure of an expression:

Wolfram Language code: Integrate[1 / (x ^ 3 - 1), x]
Wolfram Language code: Map[Framed, %, Infinity]

See Also

Apply  Scan  MapAll  MapAt  MapIndexed  MapApply  MapThread  SubsetMap  AssociationMap  KeyMap  KeyValueMap  ParallelMap  Level  Operate  Comap  Through  Thread  ImageApply

Function Repository: MapCases  MapBatched  JoinMap

Tech Notes

    ▪
  • Applying Functions to Parts of Expressions

Related Guides

    ▪
  • Applying Functions to Lists
  • ▪
  • Parts of Matrices
  • ▪
  • List Manipulation
  • ▪
  • Functional Programming
  • ▪
  • Wolfram Language Syntax
  • ▪
  • Expressions
  • ▪
  • Parts of Expressions
  • ▪
  • Associations
  • ▪
  • Function Composition & Operator Forms
  • ▪
  • Looping Constructs
  • ▪
  • Handling Arrays of Data
  • ▪
  • Language Overview
  • ▪
  • Incrementals

Related Links

  • Fast Introduction for Programmers: Applying Functions
  • An Elementary Introduction to the Wolfram Language : Ways to Apply Functions
  • NKS|Online  (A New Kind of Science)

History

Introduced in 1988 (1.0) | Updated in 2003 (5.0) ▪ 2014 (10.0)

Wolfram Research (1988), Map, Wolfram Language function, https://reference.wolfram.com/language/ref/Map.html (updated 2014).

Text

Wolfram Research (1988), Map, Wolfram Language function, https://reference.wolfram.com/language/ref/Map.html (updated 2014).

CMS

Wolfram Language. 1988. "Map." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Map.html.

APA

Wolfram Language. (1988). Map. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Map.html

BibTeX

@misc{reference.wolfram_2026_map, author="Wolfram Research", title="{Map}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/Map.html}", note=[Accessed: 01-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_map, organization={Wolfram Research}, title={Map}, year={2014}, url={https://reference.wolfram.com/language/ref/Map.html}, note=[Accessed: 01-September-2026]}

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