Is it ethical to ask a graduate student to help me with my paid external research? I have a part-time outside job in addition to being a full-time professor.  I'm struggling with performing an analysis that I believe a graduate student would be able to help me with.  I suspect the student would be happy to do so, both because  of having a nice demeanour and also they enjoy interesting problems and are also applying to PhD programs, so being able to state that they helped me with my research would be to their benefit.  I'm not able to easily get my outside employer to hire them as a consultant.  Would it be ethical for me to ask for their help with this problem?  If I did, should I offer to pay them out of my own pocket (outside salary)?  Should I insist on doing so?  I'm thinking it would take a few hours.  FWIW, I'm not their official advisor, although my colleagues and I share that role in practice.

FWIW, one of the two outside organizations involved in this project is a non-profit, for which some people volunteer the time.  (I'm being paid by a for-profit company to do work with a non-profit organization they support.)

UPDATE

After posting the question but before getting any replies, I emailed the student, asking them if they wanted to help, including a link to this question and cc'ing the director of the graduate program and the Provost, as a check on myself.

I just figured out the technical problem I was struggling with, so I no longer need help, and this question is moot.  I'll leave this question up, in case it's useful to future readers.
Before anything else, you need to be certain about the legal ground on which you stand:


Is the external work that you are doing bound by any sort of non-disclosure agreement or other agreement to which your interactions with the student would be subject?
Do the university's terms of employment for the student state anything that whether a student can work externally and under what conditions?


If it's clear from both sides, then if the student will be doing a non-trivial amount of consulting work, they should get paid just like you are getting paid.  Almost certainly, they should get paid by the company you are paid by, and not by you (unless you are doing your own work as an LLC or some such entity).  A good litmus test is: would I be doing this work for free?  Clearly, you aren't.

If it were five minutes of work, that might be different.  But if it's complex enough that you are struggling with it, it's likely to take hours, maybe many hours, and could impact your students progress in classes or other research projects.  In that case, pay is clearly deserved.