Calculate distance to RFID tag?

It is possible. As far as I know the company below (I'm not working there, I just happen to know someone who worked there a year before):

http://www.lambda4.com/

is working on such a technology.

It is possible, but to what extent end precision depends on a lot of factors: reader and tag performance, the quality of the software and the resources you are willing to invest in such a software (both time and people in R&D).

There are mainly two ways this can be achieved: The first one relies on getting the RSSI, which is basically the signal strength. The main difficulty using this indicator is that signal strength depends on a lot of factors that can influence it like, reflections if the signal needs to pass a wood cabinet or a wall, the quality of the tag, etc.

The second one is use the time the response is received to an enquiry (Time Differece of Arrival between tags). Given that you know the speed of the beam you can estimate the distance given a very precise timer. The problem here is that this also is influenced by a lot of factors: the mean time the tag needs to complete a cycle (which you should know, and should be the same for every tag used), the timer precision which is not built precisely for these purposes.

Naturally a combination of both should be employed for maximum precission and both are actually used by companies that rely on these algorithms to provide RTLS (Real Time Location Systems) application through Triangulation and Trilateration.

For further information you can check: RTLS, RSSI, TDOA, Trilateration (and Multilateration).