gives a list of the successive accumulated totals of elements in list.

Details and Options


open allclose all

Basic Examples  (2)

Cumulative sums:

Accumulate within columns:

Scope  (3)

Accumulate a regularly sampled TimeSeries:

The created time stamps are regularly spaced:



Compare to the accumulated values:

Accumulate an irregularly sampled time series:

Accumulate values:

Or define a new time series and set TemporalRegularity to True:

The path has not changed:

Now the result of Accumulate is given as a TimeSeries:

Accumulate data involving quantities:

Generalizations & Extensions  (1)

The head does not need to be List:

Applications  (4)

Triangular numbers:

Random walk:

Idealized random mountainside:

Cumulative sums of terms in a series:

Properties & Relations  (3)

Differences is almost the inverse of Accumulate:

Accumulate is equivalent to a particular case of FoldList:

Use Sum to symbolically accumulate sequences:

Possible Issues  (1)

Accumulating directly an irregularly sampled time series may differ from accumulating the values:


Check if regularly sampled:

Accumulate the time series:

This is not the same as the accumulated values:

The time series was first upsampled according to MinimumTimeIncrement and then downsampled:

Assume temporal regularity to simply accumulate the values:

Neat Examples  (1)

Diagonals of Pascal's triangle:

Wolfram Research (2007), Accumulate, Wolfram Language function, (updated 2008).


Wolfram Research (2007), Accumulate, Wolfram Language function, (updated 2008).


Wolfram Language. 2007. "Accumulate." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008.


Wolfram Language. (2007). Accumulate. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_accumulate, author="Wolfram Research", title="{Accumulate}", year="2008", howpublished="\url{}", note=[Accessed: 21-June-2024 ]}


@online{reference.wolfram_2024_accumulate, organization={Wolfram Research}, title={Accumulate}, year={2008}, url={}, note=[Accessed: 21-June-2024 ]}