So... is Big Order (TV) finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished before the manga:
Anime finished: June 18, 2016
Manga finished: August 26, 2016
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Big Order follows Eiji Hoshimiya, a high schooler burdened by a mysterious past. Ten years prior, his wish granted by a fairy triggered a global catastrophe known as the Great Destruction.
Now, he's haunted by the event and trying to care for his ailing sister. He doesn't remember the wish itself, only its devastating consequences.
In the aftermath, numerous individuals called "Orders" have emerged, each possessing unique abilities tied to their own desires. Viewed with suspicion and resentment, these Orders are often hunted.
Eiji finds himself a target of Orders seeking revenge for the Great Destruction, forcing him to confront his past and the potential dangers he unwittingly unleashed. He must learn to survive while grappling with the mystery of his forgotten wish and its connection to the world's devastation.