The number is psychiatrists per 100,000. Data from
Dartmouth Health Atlas. If you make simplifying assumptions, you can get an idea what that means. 1 in 6 people lives with mental illness (currently, not lifetime prevalence.) So if in your city there are 10 psychiatrists per 100,000 people, that means 1 psychiatrist per 10,000 people, and 1 psychiatrist for 1,667 people with mental illness. How long would it take to see them? The most under- and over-served areas are Oxford, Mississippi with 3.4 psychiatrists per 100,000 and San Luis Obispo, California with 36.5 psychiatrists per 100,000. (although I'll wager the later is counting psychiatrists at Atascadero State Hospital.) If you assume all these people being seen on an outpatient basis, by psychiatrists working 48 weeks a year, 5 days a week, with 16-30 minute shifts per day about 2/3 full, then in San Luis Obispo you could see your whole share in a little over 2 months (that is, the average follow-up time would be two months.) In Oxford it would be just under
two years.
You'll note the long tail, which begins right around 15 per 100,000, and those locations are: Morristown NJ, Alameda County (Bay Area) CA, New Orleans LA, Honolulu HI, Springfield MA, Durham NC, Santa Cruz CA, Ridgewood NJ, Hartford CT, Portland ME, Hackensack NJ, Lebanon NH, East Long Island NY, Pueblo CO, Evanston IL, Baltimore MD, Washington DC, Bridgeport CT, New Haven CT, Bronx NY, San Mateo County (Bay Area) CA, Boston MA, Manhattan NY, San Francisco CA, White Plains NY, Napa CA, and San Luis Obispo CA. There's an obvious bias toward cities with academic centers and/or places where white collar workers like to live, although the last two locations (at least) also have large state psychiatric hospitals.