# Total

Total[list]

gives the total of the elements in list.

Total[list,n]

totals all elements down to level n.

Total[list,{n}]

totals elements at level n.

Total[list,{n1,n2}]

totals elements at levels n1 through n2.

# Details and Options

• Total[list] is equivalent to Apply[Plus,list]. »
• Total[list,Infinity] totals all elements at any level in list. »
• For a 2D array or matrix: »
•  Total[list] or Total[list,{1}] totals for each column Total[list,{2}] totals for each row Total[list,2] overall total of all elements
• By default, Total only adds up elements inside List, Association and special array representations like SparseArray, SymmetrizedArray and QuantityArray. Total[,AllowedHeads->heads] will add up elements inside other expressions. Possible settings for heads include:
•  Automatic add up elements inside List, Association and special array representations Inherited add up elements inside Head[expr] All add up elements inside any normal expression Association add up the values in Association List adds up elements in lists h add up elements inside h {h1,…} add up elements inside any of h1,…
• Total[list,Method->"CompensatedSummation"] uses compensated summation to reduce numerical error in the result. »
• Total works with SparseArray objects. »

# Examples

open allclose all

## Basic Examples(1)

Total the values in a list:

## Scope(6)

Use exact arithmetic to total the values:

Use machine arithmetic:

Use 47-digit precision arithmetic:

Total the columns of a matrix:

Total the rows:

Total all the elements:

Total by adding parts in the first dimension:

Total in the last dimension only:

Total in the last two dimensions:

Total all but the last dimension:

Total all the elements:

Total the last dimension in a ragged array:

Total all the elements:

You cannot total in the first dimension because the lists have incompatible lengths:

Total the columns in a sparse matrix:

Total the rows:

Total several sparse vectors:

Total all the elements in all the vectors:

## Options(2)

### Method(1)

Use Method->"CompensatedSummation" to reduce accumulated errors in a sum:

Without compensated summation, small errors may accumulate with each term:

Find the total derivative order:

## Applications(3)

Form a polynomial from monomials:

Show that the trace of a matrix is equal to the total of its eigenvalues:

Search for "perfect" numbers equal to the sum of their divisors:

## Properties & Relations(2)

Total[list] is equivalent to Apply[Plus,list]:

Total[list,k] is equivalent to Total[Flatten[list,k-1]]:

Wolfram Research (2003), Total, Wolfram Language function, https://reference.wolfram.com/language/ref/Total.html (updated 2019).

#### Text

Wolfram Research (2003), Total, Wolfram Language function, https://reference.wolfram.com/language/ref/Total.html (updated 2019).

#### CMS

Wolfram Language. 2003. "Total." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/Total.html.

#### APA

Wolfram Language. (2003). Total. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Total.html

#### BibTeX

@misc{reference.wolfram_2024_total, author="Wolfram Research", title="{Total}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Total.html}", note=[Accessed: 13-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_total, organization={Wolfram Research}, title={Total}, year={2019}, url={https://reference.wolfram.com/language/ref/Total.html}, note=[Accessed: 13-August-2024 ]}