Some places tend to have much more intense income inequality than others. A high-income family might earn 15 or 16 times what a low-income family earns in San Francisco or Boston, compared with earnings multiples of six or eight in places like Virginia Beach or Wichita.

Low-inequality cities, the study found, tend to be located in the South and the Midwest. They also tend to be geographically large, encompassing neighborhoods that in many other cities would be considered suburbs. Generally, the average for the top income group in such cities tends to be lower than it is in high-inequality cities — $150,000 to $200,000 a year, compared with $354,000 in San Francisco and $280,000 in Atlanta.

The driving force behind spiraling inequality at a national level is the rich getting richer. But in many cases, the Brookings numbers indicated, poverty is as important a factor at the local level. In Miami, for instance, a household in the bottom 20th income percentile earned just $10,000 a year in 2012.

Inequality in the 50 biggest cities grew modestly from 2007 to 2012, the study found. The effect was not primarily because of rapid income growth among the richest families — generally, earnings for the top 1 percent of the income distribution have not yet surpassed their prerecession peak. Rather, it was because poor families, saddled with debt and high unemployment rates, have suffered through the recession and the recovery.

The single biggest increase in inequality over that period occurred in San Francisco, where earnings for the typical low-income household dropped $4,000 and soared $28,000 in inflation-adjusted dollars for a high-income household. But in most other places, inequality intensified because the poor got poorer, including in Cleveland, Sacramento, Tucson and Fresno, Calif.

“High-income households did not lose much ground during the recession,” Mr. Berube of Brookings said. “Low-income households lost ground and haven’t gained it back. And the pressures around cost of living are higher at the low end than they are at the high end.”

Researchers say local inequality trends are related to national inequality trends, but are not the same. Any individual city’s earnings ratios might be more defined by who can afford to and wants to live there — whether a family of relatively low-skilled new immigrants, or a computer programmer in high demand or a financier from abroad — than by tidal economic trends like unionization and technological change.

But New York and many other cities have promised to tackle inequality, in part by shifting the tax burden, but also through initiatives aimed at attracting middle-class families with cheaper housing and better schools.