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$MaxMachineNumber—Wolfram Documentation

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$MaxMachineNumber

is the largest machine‐precision number that can be used on a particular computer system.

Details
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Examples  
Basic Examples  
Scope  
Properties & Relations  
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$MaxMachineNumber

$MaxMachineNumber

is the largest machine‐precision number that can be used on a particular computer system.

Details

  • Numbers larger than $MaxMachineNumber are always represented in arbitrary‐precision form.
  • $MaxMachineNumber is typically 2n, where n is the maximum exponent that can be used in the internal representation of machine‐precision numbers.

Examples

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Basic Examples  (1)

The largest hardware floating point number:

Wolfram Language code: $MaxMachineNumber

Scope  (2)

Numbers larger than $MaxMachineNumber are represented as arbitrary precision numbers:

Wolfram Language code: x = 2 * $MaxMachineNumber
Wolfram Language code: {MachineNumberQ[x], Precision[x]}

Find the maximum machine number algorithmatically:

Wolfram Language code: x = 1. - $MachineEpsilon / 2; While[MachineNumberQ[x], y = x;x *= 2]; y
Wolfram Language code: y - $MaxMachineNumber

Properties & Relations  (2)

$MaxMachineNumber has the largest possible binary exponent and all bits set to 1:

Wolfram Language code: RealDigits[$MaxMachineNumber, 2]

$MaxMachineNumber×$MinMachineNumber is 4.×(1.-$MachineEpsilon/2):

Wolfram Language code: p = $MaxMachineNumber×$MinMachineNumber
Wolfram Language code: p - 4.(1. - $MachineEpsilon / 2)
Wolfram Research (1991), $MaxMachineNumber, Wolfram Language function, https://reference.wolfram.com/language/ref/$MaxMachineNumber.html.

Text

Wolfram Research (1991), $MaxMachineNumber, Wolfram Language function, https://reference.wolfram.com/language/ref/$MaxMachineNumber.html.

CMS

Wolfram Language. 1991. "$MaxMachineNumber." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/$MaxMachineNumber.html.

APA

Wolfram Language. (1991). $MaxMachineNumber. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/$MaxMachineNumber.html

BibTeX

@misc{reference.wolfram_2026_$maxmachinenumber, author="Wolfram Research", title="{$MaxMachineNumber}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/$MaxMachineNumber.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_$maxmachinenumber, organization={Wolfram Research}, title={$MaxMachineNumber}, year={1991}, url={https://reference.wolfram.com/language/ref/$MaxMachineNumber.html}, note=[Accessed: 14-November-2026]}