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PowerRange[b]

generates the list {1,10,100,…,max}, where max is the largest power of 10 that does not exceed b.

PowerRange[a,b]

generates the list {a,10a,100a,…,max}, with successive elements increasing by factors of 10.

PowerRange[a,b,r]

uses factors of r instead of 10.

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

PowerRange[b]

generates the list {1,10,100,…,max}, where max is the largest power of 10 that does not exceed b.

PowerRange[a,b]

generates the list {a,10a,100a,…,max}, with successive elements increasing by factors of 10.

PowerRange[a,b,r]

uses factors of r instead of 10.

Details

  • PowerRange effectively behaves like Range, but in "log-space".
  • The arguments a and b to PowerRange need not be integers or powers of r, but must be either both positive or both negative.
  • PowerRange starts from a and successively multiplies by r until the result is larger than b.
  • If b/a is not a power of r, the endpoint b will not be included in the list generated by PowerRange. »

Examples

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Basic Examples  (2)

Generate a list of powers of 10 from 1 to 1 million:

Wolfram Language code: PowerRange[10 ^ 6]

Start the list at 1 thousand:

Wolfram Language code: PowerRange[10 ^ 3, 10 ^ 6]

Generate a list of powers of 2 less than a hundred:

Wolfram Language code: PowerRange[1, 100, 2]

Scope  (5)

Specify a power other than 10:

Wolfram Language code: PowerRange[10, 5000, 5]

The endpoint 5000 is not included since the ratio of endpoints is not an integer power of 5:

Wolfram Language code: Log[5, (5000/50)]//N

Use a ratio whose magnitude is less than 1:

Wolfram Language code: PowerRange[2, 1 / 8, 1 / 2]

Use a negative ratio; the cutoff is determined by magnitude only:

Wolfram Language code: PowerRange[10, 10000, -5]

A range with negative numbers:

Wolfram Language code: PowerRange[-1, -5000]

Parameters need not be numeric:

Wolfram Language code: PowerRange[a, a ^ 10, a]
Wolfram Language code: PowerRange[y / x ^ 2, y * x ^ 2, x]
Wolfram Language code: PowerRange[1, x^10, Sqrt[x]]

Properties & Relations  (4)

PowerRange produces lists whose elements have a constant ratio:

Wolfram Language code: PowerRange[1, 125, 5]
Wolfram Language code: Ratios[%]

Range produces lists whose elements have a constant difference:

Wolfram Language code: Range[0, 25, 5]
Wolfram Language code: Differences[%]

For positive a and b, PowerRange[a,b] equals 10^Range[Log10[a],Log10[b]]:

Wolfram Language code: PowerRange[5, 5000] == 10 ^ Range[Log10[5], Log10[5000]]//Quiet

If moreover r>1, PowerRange[a,b,r] equals r^Range[Log[r,a],Log[r,b]]:

Wolfram Language code: PowerRange[1, 1000, 2] == 2 ^ Range[Log[2, 1], Log[2, 1000]]//Quiet

PowerRange can be implemented with NestWhileList:

Wolfram Language code: PowerRange[1, 1000000]
Wolfram Language code: NestWhileList[10#&, 1, # < 1000000&]

PowerRange produces an explicit list of values with a constant ratio:

Wolfram Language code: PowerRange[5, 10000, 7]

RSolveValue generates a formula for generating such a list:

Wolfram Language code: RSolveValue[{a[n + 1] == 7a[n], a[1] == 5}, a[n], n]
Wolfram Language code: Table[%, {n, 4}]
Wolfram Research (2014), PowerRange, Wolfram Language function, https://reference.wolfram.com/language/ref/PowerRange.html.

Text

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

CMS

Wolfram Language. 2014. "PowerRange." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PowerRange.html.

APA

Wolfram Language. (2014). PowerRange. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PowerRange.html

BibTeX

@misc{reference.wolfram_2026_powerrange, author="Wolfram Research", title="{PowerRange}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/PowerRange.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_powerrange, organization={Wolfram Research}, title={PowerRange}, year={2014}, url={https://reference.wolfram.com/language/ref/PowerRange.html}, note=[Accessed: 13-June-2026]}