More than 145,000 city children — roughly one in five — between 6 and 12 struggle with mental illness or other emotional woes, a new study has found.

The city Health Department’s analysis shows that 6 percent of kids in that age range have been diagnosed with ADHD, depression, bipolar disorder, anxiety and other behavioral problems. That’s 44,000 children.

A survey of parents also reveals that 14 percent of undiagnosed kids — about 101,000 children in that age group — “have difficulties with emotions, concentration, behavior or getting along with others.”

Furthermore, it’s likely that the severity of mental-health problems among youngsters is even worse than indicated. Survey limitations don’t capture the full extent of the problem, officials said.

“Undiagnosed conditions were not captured in Child Community Health Survey data. Therefore, prevalence estimates . . . likely underestimate true rates of mental-health conditions,” the study said.

Officials said mental illness is underreported because social stigma prevents parents from seeking help, they don’t recognize certain behaviors as a mental-health problem, or the child’s behavior does not interfere with others. Also, access to a health-care professional may be limited.

The survey, based on 2009 data and funded with support from singer Paul Simon’s Children’s Health Fund, showed that:

* ADHD was the most common diagnosis: 4 percent, or 26,000 children.

* Oppositional defiant disorder/conduct disorder was the second-most common: 2 percent, or 15,000 children.

* Boys are three times more likely than girls to be diagnosed with a mental illness — 9 percent to 3 percent.

The study pointed to lapses in treatment. Only two-thirds of kids with a mental-disorder diagnosis received medical help in the prior year, including 36 percent who received medication. Only 17 percent of kids whose parents identified them as having behavioral problems got assistance.

Identification and treatment of mental illness is crucial in helping children adapt and function.

For example, children with behavioral problems were six times more likely to have a learning disability in school and twice as likely to suffer from other health ailments, such as asthma and sleep deprivation.

The Health Department insisted the city rates were in line with national figures. The department also said it offers extensive mental services through its Family Resource Centers and public-school clinics.

It encourages families to call the 24-hour hot line LifeNet (1-800-543-3638) to connect to services.

“Over 400 schools offer mental-health services, either as part of school-based health centers or via dedicated mental-health clinics,” said a Health Department spokesman, Sam Miller.