Accumulate
✖
Accumulate
Details and Options

- Accumulate[list] has the same length as list.
- Accumulate[list] is effectively equivalent to FoldList[Plus,list].
- Accumulate[list,Method"CompensatedSummation"] uses compensated summation to reduce numerical error in the result.
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Scope (3)Survey of the scope of standard use cases
Accumulate a regularly sampled TimeSeries:

https://wolfram.com/xid/0bim3s68-iaswcf

The created time stamps are regularly spaced:

https://wolfram.com/xid/0bim3s68-75eiba


https://wolfram.com/xid/0bim3s68-ffhpdi


https://wolfram.com/xid/0bim3s68-zzbwtv

Compare to the accumulated values:

https://wolfram.com/xid/0bim3s68-jlg7lo

Accumulate an irregularly sampled time series:

https://wolfram.com/xid/0bim3s68-eaap69

https://wolfram.com/xid/0bim3s68-orapnb


https://wolfram.com/xid/0bim3s68-0pe7hg

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

https://wolfram.com/xid/0bim3s68-bq1wtd

https://wolfram.com/xid/0bim3s68-vwt5pg

Now the result of Accumulate is given as a TimeSeries:

https://wolfram.com/xid/0bim3s68-4sligq


https://wolfram.com/xid/0bim3s68-sozzs9

Accumulate data involving quantities:

https://wolfram.com/xid/0bim3s68-jopin9


https://wolfram.com/xid/0bim3s68-e8c21s

Generalizations & Extensions (1)Generalized and extended use cases
Applications (4)Sample problems that can be solved with this function

https://wolfram.com/xid/0bim3s68-hvz


https://wolfram.com/xid/0bim3s68-pnp

Idealized random mountainside:

https://wolfram.com/xid/0bim3s68-q7y

Cumulative sums of terms in a series:

https://wolfram.com/xid/0bim3s68-d3m


https://wolfram.com/xid/0bim3s68-r90

Properties & Relations (3)Properties of the function, and connections to other functions
Differences is almost the inverse of Accumulate:

https://wolfram.com/xid/0bim3s68-pzp


https://wolfram.com/xid/0bim3s68-ron

Accumulate is equivalent to a particular case of FoldList:

https://wolfram.com/xid/0bim3s68-r1cfi4


https://wolfram.com/xid/0bim3s68-c4j50b

Use Sum to symbolically accumulate sequences:

https://wolfram.com/xid/0bim3s68-d7nisi


https://wolfram.com/xid/0bim3s68-gpv83r


https://wolfram.com/xid/0bim3s68-jkb3xs

Possible Issues (1)Common pitfalls and unexpected behavior
Accumulating directly an irregularly sampled time series may differ from accumulating the values:

https://wolfram.com/xid/0bim3s68-05600o


https://wolfram.com/xid/0bim3s68-r3cdme


https://wolfram.com/xid/0bim3s68-f7t9o2


https://wolfram.com/xid/0bim3s68-436vzi


https://wolfram.com/xid/0bim3s68-qy7v2q

This is not the same as the accumulated values:

https://wolfram.com/xid/0bim3s68-zv6jlj

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

https://wolfram.com/xid/0bim3s68-mywjl7


https://wolfram.com/xid/0bim3s68-bj45tc

Assume temporal regularity to simply accumulate the values:

https://wolfram.com/xid/0bim3s68-nsw4xs


https://wolfram.com/xid/0bim3s68-zx0zql


https://wolfram.com/xid/0bim3s68-e7u51s


https://wolfram.com/xid/0bim3s68-srogth


https://wolfram.com/xid/0bim3s68-xcl0y2

Wolfram Research (2007), Accumulate, Wolfram Language function, https://reference.wolfram.com/language/ref/Accumulate.html (updated 2008).
Text
Wolfram Research (2007), Accumulate, Wolfram Language function, https://reference.wolfram.com/language/ref/Accumulate.html (updated 2008).
Wolfram Research (2007), Accumulate, Wolfram Language function, https://reference.wolfram.com/language/ref/Accumulate.html (updated 2008).
CMS
Wolfram Language. 2007. "Accumulate." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/Accumulate.html.
Wolfram Language. 2007. "Accumulate." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/Accumulate.html.
APA
Wolfram Language. (2007). Accumulate. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Accumulate.html
Wolfram Language. (2007). Accumulate. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Accumulate.html
BibTeX
@misc{reference.wolfram_2025_accumulate, author="Wolfram Research", title="{Accumulate}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Accumulate.html}", note=[Accessed: 30-April-2025
]}
BibLaTeX
@online{reference.wolfram_2025_accumulate, organization={Wolfram Research}, title={Accumulate}, year={2008}, url={https://reference.wolfram.com/language/ref/Accumulate.html}, note=[Accessed: 30-April-2025
]}