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$MachinePrecision

gives the number of decimal digits of precision used for machine‐precision numbers.

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$MachinePrecision

$MachinePrecision

gives the number of decimal digits of precision used for machine‐precision numbers.

Details

Examples

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Basic Examples  (1)

Hardware machine precision used for floating point computation:

Wolfram Language code: $MachinePrecision

Scope  (1)

Machine number approximating :

Wolfram Language code: N[Pi, MachinePrecision]

Arbitrary precision number approximating with the same precision as machine numbers:

Wolfram Language code: N[Pi, $MachinePrecision]

Applications  (1)

Make sure computations are carried out with the same precision as machine numbers:

Wolfram Language code: Block[{$MinPrecision = $MachinePrecision, $MaxPrecision = $MachinePrecision}, Exp[1000.] - Exp[1001.]]

Without fixing the precision, the resulting precision may be lower:

Wolfram Language code: Exp[1000.] - Exp[1001.]

Properties & Relations  (3)

$MachinePrecision evaluates to a number while MachinePrecision is a numerical constant:

Wolfram Language code: {$MachinePrecision, MachinePrecision}

$MachinePrecision is numerically Equal to MachinePrecision:

Wolfram Language code: $MachinePrecision == MachinePrecision

$MachinePrecision is the machine precision approximation to MachinePrecision:

Wolfram Language code: N[{$MachinePrecision, MachinePrecision}]
Wolfram Language code: N[{$MachinePrecision, MachinePrecision}, 30]

Numbers with just a few digits entered are assumed to have machine precision:

Wolfram Language code: x = 1.23456789

Precision is based on the number of digits when more than ⌈$MachinePrecision⌉+1 are entered:

Wolfram Language code: y = 1.234567890123456789
Wolfram Language code: {Precision[x], Precision[y]}

$MachinePrecision times the number of bits per digit gives the binary machine precision:

Wolfram Language code: $MachinePrecision * Log[2., 10.]

Possible Issues  (1)

$MachinePrecision uses arbitrary precision computations with machine precision resolution:

Wolfram Language code: ode = {x''[t] + Sin[x[t]] == 0, x[0] == 1, x'[0] == 0};
Wolfram Language code: asol = NDSolve[ode, x, {t, 0, 10 ^ 3Pi}, WorkingPrecision -> $MachinePrecision, MaxSteps -> Infinity]//Timing

MachinePrecision uses machine number computations:

Wolfram Language code: msol = NDSolve[ode, x, {t, 0, 10 ^ 3Pi}, WorkingPrecision -> MachinePrecision, MaxSteps -> Infinity]//Timing
Wolfram Research (1991), $MachinePrecision, Wolfram Language function, https://reference.wolfram.com/language/ref/$MachinePrecision.html (updated 2003).

Text

Wolfram Research (1991), $MachinePrecision, Wolfram Language function, https://reference.wolfram.com/language/ref/$MachinePrecision.html (updated 2003).

CMS

Wolfram Language. 1991. "$MachinePrecision." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/$MachinePrecision.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_$machineprecision, author="Wolfram Research", title="{$MachinePrecision}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/$MachinePrecision.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_$machineprecision, organization={Wolfram Research}, title={$MachinePrecision}, year={2003}, url={https://reference.wolfram.com/language/ref/$MachinePrecision.html}, note=[Accessed: 13-June-2026]}