Are there any age limits (formal, informal, or guidelines) that schools use when deciding to accept someone into a PhD program? I'm most curious about the upper age limits. For example, will most schools accept someone in their 40's? How about their 50's?
I would imagine most institutions would consider it discriminatory to judge on age, and in some places it would just be illegal. The real consideration is always whether the prospective candidate has a reasonable chance of success. Having appropriate education, or a reasonable substitute is of course the main criterion, though demonstrating research-level ability always helps (research publications etc.).
Personally I have seen PhD candidates of all ages. There's some skew to the distribution across disciplines (business and history for example often have higher proportions of older doctoral candidates than, say, mathematics), but this seems to be more a socio-cultural thing than any institutional influence.
At the university where I work, there are no limitations or guidelines on appropriate age ranges for a Ph.D., and I'm sure this is true throught the US since age discrmination would be illegal. In practice, we see the opposite problem regarding age: the application rate in mathematics is very low after the mid-20's, although we would be happy to consider older candidates. It may be that they just aren't interested in applying (if you have a family or are used to earning a high salary, then going back to school may be difficult or unappealing; furthermore, everyone is exposed to enough math in childhood that perhaps relatively few people first discover a fascination with it at an older age). However, I fear that there are people who would really like to go back and get a Ph.D., but who do not apply, because they believe they are too old to do mathematics research or because they do not believe they will be admitted. That would be sad, since I've known several extremely successful mathematicians who entered grad school well beyond the typical age.
This is a slightly different view of some issues raised in a recent answer.
That answer stated some of the disadvantages of being a mature PhD student, but missed several major advantages that mature students can have, especially if they have worked in their field of study.
I worked in the computer industry from 1970 to 2002, when I left to become a CS graduate student, completing my PhD in 2009.
Long hours. The article asked "Are you ready to pull all-nighters and push yourself to the limit (mentally and physically)?". I was definitely not ready to pull all-nighters, and never needed to. I had spent decades on projects far more complicated than one student's studies, and knew better than to leave a hard-deadline task until just before the deadline.
Over-long working hours lead to mistakes and reduced productivity. It is much more efficient to mix work with plenty of sleep and a reasonable amount of exercise and relaxation. Mature students have had more time to get work-life balance under control than recent graduates.
Not well paid. The article seemed to assume financial dependence on the PhD program. That is true for most recent graduates. Mature students, especially after successful careers in a technical field, may have other financial resources. I supported myself and paid my tuition out of my investment income while living in a house I owned.
Background knowledge. This is the area where a mature student may have the biggest advantage. There is an immense difference between passing an undergraduate course in a topic and spending several years of one's working life living and breathing it.
Staying employable in the computer industry for decades requires continuous study. I had already read some of the assigned papers for seminar courses, and earlier editions of a couple of course textbooks. Studying was easier in college because I could get advice on what to read, saving me the effort of working out what I was going to need to know next year.
After the PhD. In my case I took a year off to celebrate after the PhD, and enjoyed it so much I retired. I can still use my skills answering questions on StackOverflow, helping a college robotics team, and participating in open source software development. That is an option I would not have had thirty years earlier.
If I had looked for paid work, I would not have considered jobs as a postdoc or similar. That would ignore almost all of my resume. I was more likely to return to industry, because I prefer a pure technical path that the academic world does not seem to offer.
I know this is an older question but recently similar questions have popped up. So, I'll give my input as a recently graduated PhD.
My answer: It's never late to do a PhD, but you need to be well informed what you are signing up for. I explain.
Long hours. During my PhD I needed to work crazy hours. It's a creative process that can consume all your time. I was thinking about my work day and night. It's easy to say that I'll work 8-5 on my PhD, but I don't know any PhD student that managed to do that. You can count for lost weekends, lost vacations, sleepless nights before the big conference deadline, etc. Are you ready to pull all-nighters and push yourself to the limit (mentally and physically)? Is your family ready to accept this state of living? Will your wife/children (if any) show understanding?
Not well paid. Then, it's the financial part. Some PhD positions are well-paid, some positions (e.g. in most UK unies) you just survive, and other are unpaid. At the age of XX, you are probably used to some specific quality of life. Are you willing to sacrifice this for doing a PhD? If the position is paid, then does the salary cover your current expenses? If it's unpaid, do you have the financial resources to support yourself and your family for 4-5 years?
Background knowledge. How up-to-date are you with the current developments in your field? Many people start their PhD right after the master studies, thus they are in the studying mood and usually are up to date. You might be required to take some of those graduate level courses. These assume some background knowledge. Do you have / remember that? Especially in technical fields, you need to keep updating all the time...
After the PhD. Then it's the reason. Why do you want to do a PhD? Is it for the knowledge? After the PhD, what do you dream to do? If you plan for an academic career, you should know that you'll have to start from a lower position (postdoc, lecturer, etc.) and work your way through the ranks. Early-stage academic positions demand a huge amount of time. If you want to go for industry positions with PhD requirements, they usually have an experience requirement, so be prepared to start low.
My experiences. I believe age by itself is not a problem. I've had a colleague in his 40s doing a PhD and he did an excellent job. On the other hand another student in his 50s that gave up after 6 months. His computer skills were very bad and it was clear that he lacked (or had forgotten) key knowledge in the field (electrical engineering). Although we all tried to help him out, the pressure was too high and at the end of the day, you have to carry your own weight.
Good luck in whatever you decide!
I recall one case at Ohio State where someone who had retired from the US Army at age 55, then entered graduate school in mathematics.
Ohio State also had a program where tuition is waived for anyone over age 65 (or was it 60?). I recall a few such people taking a graduate course in math, but none working on a Ph.D.
It really depends on which institute you are attending. I did my undergrad at UC Irvine where it was very rare to see older grad students. Most grad students at UCI were accepted directly from their undergraduate programs but at the University of Nevada School of Medicine (UNSOM) where I am doing my PhD, most students have a few years of experience and so are a few years older ~30+. It never hurts to call the program head directly.
I received my PhD at the age of 65. I have a job working in my humanities profession as an adjunct and getting the expected pay for it. I have been hired for the maximum amount of hours permitted. My department chair seems to like me. My position is not a lucrative one but a retirement job. It is a job where I can research and write at my leisure without worrying about having to publish.So, jobs are out there and if being in your 30s, 40s, 50s plus is stopping you, think about what you really want from academia -- careers in teaching colleges are increasingly going on-line. The old-time professor has retreated to the nursing home. Academia is now more about corporate structure and business modeling. All academics should have updated computer skills and ready to learn anything new placed upon the desk. Publish on line. Team up with younger co-workers. Be passionate about the job at hand. In some ways, I am lucky. I do not need a tenured position. In surveying the field, I'm not sure I would want one.
If we agree that PhD holder at any level in academic position primary duty is to stimulating young scholars to correct path then expertise is vital. Consider a professor with years of experience in industry can profoundly support youth to learn meaningful objects than naïve one. the most shortage in developing countries academic education clearly is that scholars really don't know what is expecting them after graduation. skillful professor equipped with advanced theory and IT capability has profound affect positively rather very young tyro who still needs help. the best age in my opinion for PhD is in range of 35-45.