The numbers come from an examination by The Inquirer of the U.S. Census 2013 American Community Survey, released last week.
As the city's overall poverty rate declined slightly between 2012 and 2013 - from 26.9 percent to 26.3 percent - the deep-poverty rate remained nearly the same, figures show.
By definition, a family of three living in deep poverty would take in around $10,000 annually, half the poverty rate of $20,000 for a family that size.
The number of residents living in deep poverty here is roughly equivalent to the total populations of cities such as Salt Lake City; Tallahassee, Fla.; or Little Rock.
Philadelphia's deep-poverty rate "is a tremendous alarm bell of dysfunction and dangerous conditions," said Deborah Weinstein, executive director of the Coalition on Human Needs, a Washington nonprofit.
People in deep poverty live with uncertainty about food, housing, and child care, experts say. Often, they can't pay rent and move in with friends or relatives.
"When you're in deep poverty, every day is going to be the same hard grind. After a while, you stop looking for a job and settle for what life is," said Steveanna Wynn, executive director of SHARE, a Philadelphia nonprofit that distributes food to pantries in the area.
Deep poverty also has severe consequences for children. Many develop cognitive and emotional delays, studies have shown.
Children in deep poverty are more frequently hospitalized, do less well in school, and are less likely to be employed later in life, said Mariana Chilton, a national expert on poverty at Drexel University's School of Public Health.
She added that deeply impoverished children grow up to report severe depression and suicidal thoughts. Many turn to crime.
That has consequences for the city as a whole.
"Businesses will decide not to come here because we won't have enough people to employ," Chilton said.
The root cause of deep poverty is "people unable to get jobs for one reason or another," said Roberta Iversen, an expert on low-income families at the University of Pennsylvania. "They can't work for reasons of depression, disability, or lack of jobs."
Dorothy Caban, 42, was married, then separated and fell into deep poverty two years ago. She and her three children, ages 7 to 17, live in the Northeast.
Born in South Philadelphia to Irish and Italian parents, Caban dropped out of high school, then later worked as a cashier. She suffered deep depression after her second child was born and was unable to continue working. Her marriage disintegrated.
Caban receives $740 a month in disability payments from the Social Security Administration, an annual income of $8,880, well below the poverty rate of $22,607 for a family of four.
"It's very hard," said Caban, who after separating could no longer afford her $750 monthly rent. She was forced to move in with relatives not long ago. Caban said she did not receive child support because her ex-husband was not able to work.
"My youngest kids don't understand," Caban said, crying. "My 17-year-old goes to school and keeps applying for part-time jobs. He tells me, 'Don't worry, Mom.' "
But for Caban, all of life is worry.
"I never thought I'd be in this situation," she said. "We can't buy things we need, and we go to a food pantry to help us eat."
That's something that may not change soon, experts say.
"If you're in deep poverty, the odds that you'll climb out are substantially against you," said James Ziliak, economist and director of the Center for Poverty Research at the University of Kentucky.
"These people lack the skills to succeed in the labor force."