SAN FRANCISCO — The number of homeless children in the U.S. has surged in recent years to an all-time high, amounting to one child in every 30, according to a comprehensive state-by-state report that blames the nation’s high poverty rate, the lack of affordable housing and the impacts of pervasive domestic violence.

Titled “America’s Youngest Outcasts,” the report being issued Monday by the National Center on Family Homelessness calculates that nearly 2.5 million American children were homeless at some point in 2013. The number is based on the Department of Education’s latest count of 1.3 million homeless children in public schools, supplemented by estimates of homeless pre-school children not counted by the DOE.

The problem is particularly severe in California, which has one-eighth of the U.S. population but accounts for more than one-fifth of the homeless children with a tally of nearly 527,000.

Carmela DeCandia, director of the national center and a co-author of the report, noted that the federal government has made progress in reducing homelessness among veterans and chronically homeless adults.

“The same level of attention and resources has not been targeted to help families and children,” she said. “As a society, we’re going to pay a high price, in human and economic terms.”

Child homelessness increased by 8 percent nationally from 2012 to 2013, according to the report, which warned of potentially devastating effects on children’s educational, emotional and social development, as well as on their parents’ health, employment prospects and parenting abilities.

The report included a composite index ranking the states on the extent of child homelessness, efforts to combat it, and the overall level of child well-being. States with the best scores were Minnesota, Nebraska and Massachusetts. At the bottom were Alabama, Mississippi and California.

California’s poor ranking did not surprise Shahera Hyatt, director of the California Homeless Youth Project.

The crux of the problem, she said, is the state’s high cost of living, coupled with insufficient affordable housing.

“People think, ‘Of course we are not letting children and families be homeless,’ so there’s a lot of disbelief,” Hyatt said. “California has not invested in this issue.”