Counted inside city limits, the way the census counts cities, the top ten moved south and west after the Second World War. Part of that, the Census Bureau says, is where city lines are drawn : most of the rising cities took in a lot of land, and counted by whole metro areas, only three of the ten largest are in those states.

A climb over decades, not two convenient years

Every ten years the census counts the people inside each city's legal limits as they stand at census time. Count how many of the ten largest cities were in California, Texas or Arizona at each census. The number was 1 in 1900, 0 in 1910, 1 at every census of 1920–50, 2 in 1960, 3 in 1970, 5 in 1980, 6 in 1990, 6 in 2000, 7 in 2010 and 7 in 2020.

At every census for half a century, the count was never above one. San Francisco was 9th in 1900. Then Los Angeles entered at 10th in 1920 and was 4th by 1950. After 1950 a new city joined almost every decade : Houston, Dallas, San Diego and Phoenix, San Antonio, and finally San Jose. The count climbed from 1960 to 2010, with a pause in 2000, so the shift doesn't depend on picking two convenient years.

The cities that left the list did more than slip. Six of the 1950 top ten were gone by 2020 : St. Louis, Boston, Cleveland, Baltimore, Detroit and Washington. Of the 1950 ten, only New York and Los Angeles had more people in 2020 than in 1950. Detroit fell from 1.85 million to 639,000, about 65% fewer. Phoenix grew from about 107,000 to 1.6 million, roughly fifteen times as many.

The counts show the order things happened in, not why. Wikipedia's Sun Belt article, which covers Texas, Arizona and most of California, gives the usual account : growth after the war came from people "seeking a warm and sunny climate" and "growing economic opportunities", and air conditioning "allowed more manufacturing and industry to locate in the Sun Belt."

For half a century it was one city at most, then the count climbed to seven · How many of the ten largest US cities were in California, Texas or Arizona, by census from 1900 to 2020 · 1900 · 1910 · 1920–50 · 1960 · 1970 · 1980 · 1990 · 2000 · 2010 · 2020 · Top-ten cities in CA, TX or AZ · 7 · 1920 · — How many of the ten largest US cities were in California, Texas or Arizona, by census from 1900 to 2020

The lines moved too

A city's count is the people inside its borders, and some borders moved a long way. The Census Bureau's history of city rankings (Working Paper 27, 1998) says city growth "has been due partly to annexations," and that some cities, "especially in the South and West in recent decades, have had large annexations well before urban-type settlement in the annexed areas." Its tables give each city's land area in square miles.

Between 1950 and 1990, Phoenix went from 17.1 square miles to 419.9. San Antonio went from 69.5 to 333.0, Houston from 160.0 to 539.9, San Diego from 99.4 to 324.0, and Dallas from 112.0 to 342.4. Over the same years Chicago went from 207.5 to 227.2, Los Angeles from 450.9 to 469.3, and New York from 315.1 to 308.9.

So Phoenix covered about 25 times as much land in 1990 as in 1950. San Antonio, Houston, San Diego and Dallas covered three to five times as much. New York, Chicago and Los Angeles changed by less than a tenth. The paper adds that recorded area also shifts with boundary adjustments and new ways of measuring, so this data can't say how much of the rise is annexation. And land isn't the whole story : between 1950 and 1990 Los Angeles barely grew in area, while its population went from 1.97 million to 3.49 million.

The rising cities took in far more land, while the old giants barely changed · City land area in square miles, 1950 and 1990, from the Census Bureau's tables · 1950 · 1990 · Phoenix · San Antonio · Houston · San Diego · Dallas · Chicago · Los Angeles · New York · 17.1 · 69.5 · 160.0 · 99.4 · 112.0 · — City land area in square miles, 1950 and 1990, from the Census Bureau's tables

Count whole metro areas, and it's three

A metropolitan statistical area is built from whole counties (or county equivalents) : one or more central counties around a core urban area, plus outlying counties tied to them by commuting and employment. In the 2020 census, counted on the metro boundaries drawn in 2023, the ten largest were New York, Los Angeles, Chicago, Dallas–Fort Worth, Houston, Washington, Philadelphia, Miami, Atlanta and Boston. Three are in California, Texas or Arizona. Add Florida and Georgia, two more Sun Belt states, and it's five.

Which unit you count changes the ranks a lot. Phoenix is 5th as a city but 11th as a metro. San Antonio is 7th and 24th, San Jose 10th and 36th. Their city limits hold a third to over half of their metro's people (33%, 56% and 51%). Dallas runs the other way : 9th as a city but 4th as a metro, whose people mostly live outside the city of Dallas (it holds 17%). The Census paper found the same pattern with a third measure, the built-up urbanized area. In 1950 the city and urbanized-area rankings roughly matched. By 1990, "the situation had changed dramatically, due partly to differences in annexation practices"; San Antonio, for example, was 10th as a city and 31st as an urbanized area.

So both are true. Within city limits, the top ten moved decisively south and west. Counted by metro area in 2020, the three states hold three of the ten largest. That metro list is a single snapshot, so it can't show how far metros moved since 1950.