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Ratios[list]

gives the successive ratios of elements in list.

Ratios[list,n]

gives the n^(th) iterated ratios of list.

Ratios[list,{n1,n2,…}]

gives the successive nk^(th) ratios at level k in a nested list.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
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Ratios

Ratios[list]

gives the successive ratios of elements in list.

Ratios[list,n]

gives the n^(th) iterated ratios of list.

Ratios[list,{n1,n2,…}]

gives the successive nk^(th) ratios at level k in a nested list.

Details

  • Ratios divides successive elements by preceding ones, so that Ratios[{x1,x2}] gives {x2/x1}.
  • If list has length s, Ratios[list,n] has length s-n.
  • Ratios[m,{1,0}] or Ratios[m,1] finds the successive ratios of rows in a 2D array or matrix m. Ratios[m,{0,1}] finds the ratios of columns.
  • Ratios[list,{n1,n2}] is equivalent to Ratios[Ratios[list,n1],{0,n2}].

Examples

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Basic Examples  (2)

First ratios:

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

Second ratios:

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

Scope  (3)

Ratios of rows, within each column:

Wolfram Language code: Ratios[(| | | | | :-- | :-- | :-- | | a11 | a12 | a13 | | a21 | a22 | a23 | | a31 | a32 | a33 |)]//MatrixForm
Wolfram Language code: Ratios[(| | | | | :-- | :-- | :-- | | a11 | a12 | a13 | | a21 | a22 | a23 | | a31 | a32 | a33 |), {1, 0}]//MatrixForm

Ratios of columns, within each row:

Wolfram Language code: Ratios[(| | | | | :-- | :-- | :-- | | a11 | a12 | a13 | | a21 | a22 | a23 | | a31 | a32 | a33 |), {0, 1}]//MatrixForm

Ratios of a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{x[1], x[2], x[3], x[4], x[5], x[6]}}, {{0, 5, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: ts["Path"]
Wolfram Language code: ratios = Ratios[ts]
Wolfram Language code: ratios["Path"]

Properties & Relations  (2)

First ratios are constant for a geometric sequence:

Wolfram Language code: Table[2 ^ i, {i, 0, 10}]
Wolfram Language code: Ratios[%]

FoldList with Times acts as an inverse of Ratios:

Wolfram Language code: Ratios[{a, b, c, d, e}]
Wolfram Language code: FoldList[Times, a, %]
Wolfram Research (2008), Ratios, Wolfram Language function, https://reference.wolfram.com/language/ref/Ratios.html.

Text

Wolfram Research (2008), Ratios, Wolfram Language function, https://reference.wolfram.com/language/ref/Ratios.html.

CMS

Wolfram Language. 2008. "Ratios." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Ratios.html.

APA

Wolfram Language. (2008). Ratios. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Ratios.html

BibTeX

@misc{reference.wolfram_2026_ratios, author="Wolfram Research", title="{Ratios}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Ratios.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_ratios, organization={Wolfram Research}, title={Ratios}, year={2008}, url={https://reference.wolfram.com/language/ref/Ratios.html}, note=[Accessed: 13-June-2026]}