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DigitSum[n]

gives the sum of the decimal digits in the integer n.

DigitSum[n,b]

gives the sum of the base b digits in the integer n.

DigitSum[n,b,k]

gives the sum of the first k base b digits in the integer n.

DigitSum[n,b,-k]

gives the sum of the last k base b digits in the integer n.

DigitSum[n,MixedRadix[blist]]

uses the mixed radix with list of bases blist.

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DigitSum

DigitSum[n]

gives the sum of the decimal digits in the integer n.

DigitSum[n,b]

gives the sum of the base b digits in the integer n.

DigitSum[n,b,k]

gives the sum of the first k base b digits in the integer n.

DigitSum[n,b,-k]

gives the sum of the last k base b digits in the integer n.

DigitSum[n,MixedRadix[blist]]

uses the mixed radix with list of bases blist.

Details

Examples

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Basic Examples  (3)

Find the sum of the decimal digits in :

Wolfram Language code: DigitSum[58127]

Find the sum of the binary digits in :

Wolfram Language code: DigitSum[58127, 2]

Find the digit sum in a mixed radix system:

Wolfram Language code: DigitSum[102341, MixedRadix[{24, 60, 60}]]

Scope  (8)

Compute for large numbers:

Wolfram Language code: DigitSum[9 ^ 1000 + 1]

Use a base larger than 10:

Wolfram Language code: DigitSum[58127, 16]

DigitSum threads over lists:

Wolfram Language code: DigitSum[{6, 7, 2}, 2]

Find the digit sum of 7 in different bases:

Wolfram Language code: DigitSum[7, {2, 3, 4}]

Sum only the first 4 digits:

Wolfram Language code: DigitSum[6345354, 10, 4]

Sum only the last 4 digits:

Wolfram Language code: DigitSum[6345354, 10, -4]

Find digit sums using a MixedRadix specification:

Wolfram Language code: DigitSum[137, MixedRadix[{3, 12}]]

Sum only the last 2 digits:

Wolfram Language code: DigitSum[1084, MixedRadix[{17, 15, 11}], -2]

Exact values are generated at integers:

Wolfram Language code: DigitSum[35297]

Applications  (1)

Plot the sum of the digits in the first 100 positive integers:

Wolfram Language code: DiscretePlot[DigitSum[n], {n, 100}]

Properties & Relations  (9)

Use IntegerDigits to compute DigitSum:

Wolfram Language code: Total[IntegerDigits[37103]]
Wolfram Language code: DigitSum[37103]

Use HammingDistance to compute DigitSum in binary:

Wolfram Language code: HammingDistance[IntegerDigits[143, 2], 0IntegerDigits[143, 2]]
Wolfram Language code: DigitSum[143, 2]

DigitSum[n,b,-k] gives 0 when k is less than or equal to IntegerExponent[n,b]:

Wolfram Language code: DigitSum[123000, 10, -3]
Wolfram Language code: IntegerExponent[123000, 10]

In particular, DigitSum[0,b,k] is always 0:

Wolfram Language code: DigitSum[0, 10, -3]
Wolfram Language code: IntegerExponent[0]

Use DigitCount to compute DigitSum in binary:

Wolfram Language code: DigitCount[2147, 2, 1]
Wolfram Language code: DigitSum[2147, 2]

Use DigitCount to compute DigitSum in any base:

Wolfram Language code: DigitCount[2147].Mod[Range[10], 10]
Wolfram Language code: DigitSum[2147]

IntegerLength and DigitSum give for in base :

Wolfram Language code: IntegerLength[(10 ^ 17 - 1) / (10 - 1)]
Wolfram Language code: DigitSum[(10 ^ 17 - 1) / (10 - 1)]

DigitSum[n,b,k] is equivalent to DigitSum[n,b] when k is greater than the integer length of n in base b:

Wolfram Language code: DigitSum[123456, 10, 7]
Wolfram Language code: IntegerLength[123456, 10]

DigitSum gives the same result for n and IntegerReverse[n,b]:

Wolfram Language code: DigitSum[263, 5]
Wolfram Language code: DigitSum[IntegerReverse[263, 5], 5]

The sign is ignored:

Wolfram Language code: DigitSum[-3134]
Wolfram Research (2024), DigitSum, Wolfram Language function, https://reference.wolfram.com/language/ref/DigitSum.html.

Text

Wolfram Research (2024), DigitSum, Wolfram Language function, https://reference.wolfram.com/language/ref/DigitSum.html.

CMS

Wolfram Language. 2024. "DigitSum." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DigitSum.html.

APA

Wolfram Language. (2024). DigitSum. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DigitSum.html

BibTeX

@misc{reference.wolfram_2026_digitsum, author="Wolfram Research", title="{DigitSum}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/DigitSum.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_digitsum, organization={Wolfram Research}, title={DigitSum}, year={2024}, url={https://reference.wolfram.com/language/ref/DigitSum.html}, note=[Accessed: 12-June-2026]}