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Wolfram Language & System Documentation Center
Range
  • See Also
    • Table
    • Subdivide
    • CoordinateBoundsArray
    • ConstantArray
    • Interval
    • PowerRange
    • CharacterRange
    • FindDivisions
    • Clip
  • Related Guides
    • Constructing Lists
    • Regular & Coordinate Arrays
    • List Manipulation
    • Incrementals
    • Graphics Annotation & Appearance
  • Tech Notes
    • Vectors and Matrices
    • Making Tables of Values
    • See Also
      • Table
      • Subdivide
      • CoordinateBoundsArray
      • ConstantArray
      • Interval
      • PowerRange
      • CharacterRange
      • FindDivisions
      • Clip
    • Related Guides
      • Constructing Lists
      • Regular & Coordinate Arrays
      • List Manipulation
      • Incrementals
      • Graphics Annotation & Appearance
    • Tech Notes
      • Vectors and Matrices
      • Making Tables of Values

Range[imax]

generates the list {1,2,…,imax}.

Range[imin,imax]

generates the list {imin,…,imax}.

Range[imin,imax,di]

uses step di.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • Table
    • Subdivide
    • CoordinateBoundsArray
    • ConstantArray
    • Interval
    • PowerRange
    • CharacterRange
    • FindDivisions
    • Clip
  • Related Guides
    • Constructing Lists
    • Regular & Coordinate Arrays
    • List Manipulation
    • Incrementals
    • Graphics Annotation & Appearance
  • Tech Notes
    • Vectors and Matrices
    • Making Tables of Values
    • See Also
      • Table
      • Subdivide
      • CoordinateBoundsArray
      • ConstantArray
      • Interval
      • PowerRange
      • CharacterRange
      • FindDivisions
      • Clip
    • Related Guides
      • Constructing Lists
      • Regular & Coordinate Arrays
      • List Manipulation
      • Incrementals
      • Graphics Annotation & Appearance
    • Tech Notes
      • Vectors and Matrices
      • Making Tables of Values

Range

Range[imax]

generates the list {1,2,…,imax}.

Range[imin,imax]

generates the list {imin,…,imax}.

Range[imin,imax,di]

uses step di.

Details

  • The arguments to Range need not be integers.
  • Range starts from imin and successively adds increments of di until the result is greater than imax.
  • Range uses the standard Wolfram Language iteration specification, as applied to a single variable.
  • Range has attribute Listable.

Examples

open all close all

Basic Examples  (3)

Get integer values from 1 to 4:

Wolfram Language code: Range[4]

Obtain a range of numbers starting from 1.2 and stopping no later than 2.1 in steps of 0.15:

Wolfram Language code: Range[1.2, 2.2, 0.15]

A symbolic range of numbers in unit steps:

Wolfram Language code: Range[x, x + 4]

Scope  (6)

Use a step of 2:

Wolfram Language code: Range[1, 10, 2]

Use a negative step:

Wolfram Language code: Range[10, 1, -1]

Use an exact numeric-valued step:

Wolfram Language code: Range[0, 10, π]

Use a machine-number step:

Wolfram Language code: Range[0, 10, N[π]]

Use a precision-24 step:

Wolfram Language code: Range[0, 10, N[π, 24]]

Range of very large numbers:

Wolfram Language code: Range[2 ^ 225, 2 ^ 225 + 5]

Generalizations & Extensions  (2)

Use a symbolic step:

Wolfram Language code: Range[a, b, (b - a) / 4]

Use a list of range specifications:

Wolfram Language code: Range[{5, 2, 6, 3}]

Applications  (4)

Produce a geometric sequence:

Wolfram Language code: q ^ Range[5]

Form a polynomial from coefficients:

Wolfram Language code: coeff = {-2, 9, 5, 3, -3, -6, -7, -4, 8, 3};
Wolfram Language code: poly = coeff.x ^ Range[0, Length[coeff] - 1]

Form a random permutation:

Wolfram Language code: RandomSample[Range[10]]

Find an inverse permutation:

Wolfram Language code: perm = RandomSample[Range[10]]
Wolfram Language code: inverse = perm; inverse[[perm]] = Range[Length[perm]]; inverse

Properties & Relations  (2)

Range[imin,imax,di] is equivalent to Table[i,{imin,imax,di}]:

Wolfram Language code: Range[-4, 9, 3]
Wolfram Language code: Table[i, {i, -4, 9, 3}]

Use Range or Span (;;) as Part specification:

Wolfram Language code: list = {a, b, c, d, e};
Wolfram Language code: list[[Range[1, 5, 2]]]
Wolfram Language code: list[[1 ;; 5 ;; 2]]

Possible Issues  (3)

For some step sizes, Range may not include the upper limit given:

Wolfram Language code: Range[0, 10, 3]

Even though the lower limit was exact, the inexact step makes the first element inexact:

Wolfram Language code: Range[0, 1, .1]

Range accepts Quantity expressions as limits and steps:

Wolfram Language code: Range[Quantity[1, "Meters"], Quantity[9, "Meters"], Quantity[2, "Meters"]]

For Quantity expressions, Precision is taken into account when determining whether elements are within the bounds of the limits:

Wolfram Language code: Precision[UnitConvert[Quantity[1, "MagneticFineStructureConstant"]]]
Wolfram Language code: Range[Quantity[40, "MagneticFineStructureConstant"]]
Wolfram Language code: Length@%

Neat Examples  (1)

Make nested ranges:

Wolfram Language code: Range[Range[5]]
Wolfram Language code: Range[Range[Range[3]]]
Wolfram Language code: Nest[Range, 3, 6]

Show it in tree form:

Wolfram Language code: TreeForm[%]

See Also

Table  Subdivide  CoordinateBoundsArray  ConstantArray  Interval  PowerRange  CharacterRange  FindDivisions  Clip

Function Repository: SpanRange  ArithmeticProgression

Tech Notes

    ▪
  • Vectors and Matrices
  • ▪
  • Making Tables of Values

Related Guides

    ▪
  • Constructing Lists
  • ▪
  • Regular & Coordinate Arrays
  • ▪
  • List Manipulation
  • ▪
  • Incrementals
  • ▪
  • Graphics Annotation & Appearance

Related Links

  • An Elementary Introduction to the Wolfram Language : First Look at Lists
  • An Elementary Introduction to the Wolfram Language : Options
  • NKS|Online  (A New Kind of Science)

History

Introduced in 1988 (1.0)

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

Text

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

CMS

Wolfram Language. 1988. "Range." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Range.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_range, author="Wolfram Research", title="{Range}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Range.html}", note=[Accessed: 01-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_range, organization={Wolfram Research}, title={Range}, year={1988}, url={https://reference.wolfram.com/language/ref/Range.html}, note=[Accessed: 01-September-2026]}

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