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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.
  • 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
  • Total[f[e1, e2, ...]] gives the sum of the ei for any head f.  »
  • Total[list, Method->"CompensatedSummation"] uses compensated summation to reduce numerical error in the result.  »
EXAMPLESCLOSE ALL
Basic Examples   (1)
Total the values in a list:
Total the values in a list:
In[1]:=
Click for copyable input
Out[1]=
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 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:
Generalizations & Extensions   (1)
Total works with any head:
Find the total derivative order:
Options   (1)
Use Method->"CompensatedSummation" to reduce accumulated errors in a sum:
Without compensated summation, small errors may accumulate with each term:
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]]:
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