What is the smallest area containing 1/2 the US population?

Imagine, if you will, the entire US. Draw a circle around some part of the country. Some portion of the population will be inside the circle, and some outside. What is the smallest circle one can draw that contains 1/2 of the country’s population? Where is its center? I have no idea how to even go about figuring this out. You could rough-estimate it with state populations from census data, and get even closer looking at the county level. Anyone have any clue what the answer is, or even how to find it? I’m guessing the center of such a circle would be in the western south-east US, so the circle could include Chicago, NY, Boston, maybe parts of Florida.

This will be very difficult to answer given that you say “draw a circle…” – there aren’t easily available population figures for random circles on a map.

Maybe if you refined the question as:
“What is the smallest (in area) selection of contiguous US states that contains 1/2 of the US population?”

That way, someone might be able to answer it.

This would be a good first step toward the answer. After finding the smallest area contiguous states grouping, you could then proceed to locate large cities just outside those states and drop section of the original group that were more rural or less residential. My first hunch is that the northeastern states are where you’d better start. Just look at the map for the place where the smaller states are and how they get larger as you go south and then west. The population dwindles as the states get larger. Exceptions include Texas and California.

But the lack of precise data for sections of states may make the task more difficult.

I know where I’d start. I’d go about halfway between New York and Chicago and extend out from there. You would have some major population areas inside that circle. Once you got big enough to include the Washington D. C. area and Boston you would probably be pretty close to your goal.

Going by contiguous states and not a circle:

Total US population is 281,421,906 (all figures are from the 2000 census). Half of this is 140,710,953. The total land area of the United States is 3,537,438 square miles.

The top states in order of population density are:

District of Columbia - 572,059 - 61
New Jersey - 8,717,925 - 7,417
Rhode Island - 1,048,319 - 1,045
Massachusetts - 6,349,097 - 7,840
Connecticut - 3,405,565 - 4,845
Maryland - 5,296,486 - 9,774
New York - 18,976,457 - 47,214
Delaware - 783,600 - 1,954
Florida - 15,982,378 - 53,927
Ohio - 11,353,140 - 40,948
Pennsylvania - 12,281,054 - 44,817
California - 33,871,648 - 155,959
Illinois - 12,419,293 - 55,584
Hawaii - 1,211,537 - 6,423
Michigan - 9,938,444 - 56,804
Indiana - 6,080,485 - 35,867
Virginia - 7,078,515 - 39,594
North Carolina - 8,049,313 - 48,711
Georgia - 8,186,453 - 57,906
Tennessee - 5,689,283 - 41,217
New Hampshire - 1,235,786 - 8,968
South Carolina - 4,012,012 - 30,109
Louisiana - 4,468,976 - 43,562
Kentucky - 4,041,769 - 39,728

Skipping the non-contiguous ones - California, Hawaii, and Louisiana - we have 21 states (plus DC) with a combined population of 143,701,508 and a combined total area of 634,110 square miles (just over 51% of the total population in just under 18% of the total land area.)

You could also do it by metropolitan area…
http://en.wikipedia.org/wiki/List_of_United_States_metropolitan_statistical_areas_by_population

By my calculation based on these 2004 figures from wikipedia these 25 metropolitan areas contain around 120m people:

New York-Northern New Jersey-Long Island
Los Angeles-Long Beach-Santa Ana
Chicago-Naperville-Joliet
Philadelphia-Camden-Wilmington
Dallas-Fort Worth-Arlington
Miami-Fort Lauderdale-Miami Beach
Houston-Sugar Land-Baytown
Washington-Arlington-Alexandria
Atlanta-Sandy Springs-Marietta
Detroit-Warren-Livonia
Boston-Cambridge-Quincy
San Francisco-Oakland-Fremont
Riverside-San Bernardino-Ontario
Phoenix-Mesa-Scottsdale
Seattle-Tacoma-Bellevue
Minneapolis-St. Paul-Bloomington
San Diego-Carlsbad-San Marcos
St. Louis
Baltimore-Towson
Tampa-St. Petersburg-Clearwater
Pittsburgh
Denver-Aurora
Cleveland-Elyria-Mentor
Portland-Vancouver-Beaverton
Cincinnati-Middletown

I suppose drawing circles tightly around individual people and connecting them with infinitely thin stems would be cheating, huh?

There’s no question but that the circle would contain New Jersey.

Maybe going by states was too approximate. We need to trim off some of the fat around the edges.

The Upper Peninsula of Michigan (with a population of 328,000 and an area of 16,452 square miles) and New York’s North Country (with a population of 420,492 and an area of 10,699 square miles) are out, bringing our total down to 142,953,016 people (50.8%) in 606,959 square miles (17.2%).

Here’s one way of doing it.

The population center of the United States is in Phelps County, Missouri. That’s closer to the East Coast than the West Coast, so we focus on the eastern half of the Country.

Using a primitive ruler-and-map method of calculating, we see that Boston and Miami are roughly the same distance from Phelps County. So draw a circle that includes all three places.

Unfortunately, that turns out to be a freakin’ HUGE circle. Either Boston or Miami has to go. Fortunately, Minneapolis-St. Paul is roughly the same size as Miami and lies outside the original circle. Moving the circle a little north and west to give an arc between Minneapolis and Boston (it leaves out Miami but includes Tampa and Orlando) lets us shrink the circumfrence and centers us roughly at. . . Lexington, Kentucky.

Your circles may vary.

Lexington makes good sense to me in that when I was in college it was bandied about that Nashville TN was within 500 miles of over half the population of the USA. Whether that was the lower 48 or just what wasn’t specified. And I don’t know if I ever saw supportive data. In any case, Nashville, Knoxville, Lexington, Louisville, Cincinnati, and maybe even Memphis would be in the vicinity of that circle’s center. I doubt it would be much further south or west. Memphis is a push, I think.

When you think of big populations west of the Mississippi, California and Texas seem to be where you focus. Yes, there’s Denver or St. Louis, and probably another dozen cities in the top 100 population areas, but the big cities are further east and north.

Knowing that the population center is in Missouri is a definite clue that the circle you want to draw is east of that.

Not according to the rules: contiguous area