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Recently my paper got accepted in a journal. After that we submitted the final version with all corrections. Now I found an error in the way I calculated some type of numerical error. I don’t think correcting the numerical errors will change any of the conclusions of the paper.

What should I do in such a situation? Is it necessary to submit an erratum to the journal?

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    If the paper has not yet been published, contact the editor, explain the situation and ask for last-minute corrections. This will delay the publication, but you'll avoid an erratum. If the paper is already published, an erratum will be in place. – corey979 Feb 7 at 18:10
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The first thing to do is to contact the editor and ask for advice. Follow it. The second thing to do is to check the conclusions of the paper to assure yourself they they are still ok. The third thing to do is to prepare an erratum note in case it needs to be sent.

But the editor may have a solution if you are fast enough.

But if the conclusions are compromised you may need to ask if the editor can pull the paper while you go back and rethink everything.

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If your paper hasn't been accepted yet, write to the journal's editor as soon as possible. If your paper has been accepted, write to the journal office as soon as possible.

Chances are you'll be able to make this change before the paper is published, but you still want to make this known quickly. The editor will care if the mistake needs to be re-reviewed. Similarly, the publisher will care if the revisions change the layout. The first round of typesetting is the most laborious; if the revisions e.g. change the positions of figures, they might have to start work again from scratch.

The longer you wait, the more likely you'll have to write an erratum.

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