Student or Learner
"The mistake put the calculation out by a factor of 2."
"The mistake put the calculation off by a factor of 2."
Is the second one standard English?
(Not a Teacher)
I would use "threw off". I can't say I've ever heard "put off" used like this, but maybe it's BrE. Same thing for "put out", but I'm inclined to think that one is just plain wrong.