Is it generally acceptable to ask how many applicants there were to a position I applied for, and does it depend on the current stage of my application? For instance, immediately after applying, at an interview, after receiving an offer, etc.
You should generally stick to asking pertinent questions whose answers are meaningful to you, rather than asking questions simply to satisfy your own curiosity. The number of other applicants will usually not have a major effect on your own interview process, and knowing that number won't make you any more or less likely to get the job. The hiring process is usually not something that's shared outside of a company, so you may come off as asking about irrelevant information that the company would be reticent to share anyway.
I could see asking about the general number of other applicants if you're trying to get a sense of the interview process time frame. If they tell you they'll call back after a first phone interview with other applicants, it might be reasonable to ask in a general sense how many there are and if that will take days, weeks, or months. But idly asking just for the heck of it serves no real purpose, and may not be received well.
I would recommend not doing this. It is probably done rarely and when done not always responded to. The numbers also change, both up and down during the process.
But, it also makes you sound a bit desperate rather than confident.
Some places will publish some numbers from prior years, so you can get an idea.
- After a position is filled, it is fine to politely inquire about how large the applicant pool was.
- If you are interviewed or short-listed, it is fine to politely ask how many other interviewees or short-listers there are.
The basic parameters here are that you don't want to do anything to compromise your application, and you don't want to be a bother, but you do want to get information that might help you in future applications.
Asking right after applying is probably going to seem overly forward, and will probably be incorrect information since the application hasn't yet closed.
If you are (unfortunately) rejected, there is probably no downside to asking whoever communicates with you regarding the rejection how large the applicant pool was. Most hiring committees will be fine with sharing this information. The worst that will happen is that your request will be ignored.
If you advance in the process, it is OK to ask how many applicants are at the same stage. In fact, many hiring committees will proactively share this information. In academic hiring there is often a short list (on campus interviews) of 3, and applicants may want to know if the short list is more or less. Long lists are often more variable (e.g., 8 phone interviews). Hiring committees may proactively share this information (i.e. "We are doing four on campus interviews."). I might not ask this during a phone interview, but if you get an on campus interview, there is probably little harm in politely asking how large the applicant pool was. For example, "Do you mind if I ask how large the applicant pool was?" If the person asks why--and, frankly, anyone on a hiring committee will know why--you might say something like "I'm just trying to get a handle on how competitive hiring in physics/economics/English/sociology/biochemistry is this year."
In short, it's probably OK to ask, but be polite, and ask after you have advanced in the process or been rejected.