Despite a rising citywide graduation rate, the number of students with the skills to succeed in college is alarmingly low — even at some schools that hand out the most diplomas, a Post analysis found.

College readiness sunk to 1.9 percent last year at the FDNY HS for Fire and Life Safety in Brooklyn, which had an 83 percent graduation rate in 2016, city reports show.

The school, which has about 335 students, topped the list of high schools run by the Department of Education with the widest gap between graduation and college readiness rates, The Post found.

Mayor de Blasio and Schools Chancellor Carmen Fariña cite the city wide 72 percent graduation rate as evidence that schools are improving. Rarely noted — only an average 37 percent of students graduate ready for college.

That wide gap suggests some NYC high schools hand out sheepskins too freely to inflate their success.

“These disparities raise questions that need clear explanations,” said David Bloomfield, a Brooklyn College and CUNY Grad School education professor.

He said the system has long been plagued by ways to “game the graduation rates” such as quickie make-up work for students who fail courses.

But he added, “Looking at whether students enter and stay in college also needs to be examined to gauge whether the readiness rate is accurate.”

College readiness is determined when students earn minimum scores on standardized tests such as a 75 on the English Regents exam and 70 on the Common Core Math Regents exam or a minimum 530 on the math SAT or pass certain math courses. Students who meet these thresholds are expected not to need remedial help at CUNY.

City Comptroller Scott Stringer highlighted the issue in a report last September showing that college readiness rates fell at 16 percent of city schools between 2011 and 2015, with the lowest levels in the Bronx and Brooklyn.

Nearly 80 percent of New York City high school grads who enrolled as freshmen at a CUNY community college in the fall of 2015 needed remedial help in math, reading and writing, the report found.

The Post reported last month that Bronxdale HS in Allerton had a 76 percent graduation rate in 2016, but a 4 percent college readiness rate.

But the stats are even worse at other schools such as Urban Assembly HS of Music and Art in Brooklyn, which boasted a 82.5 percent graduation rate but only 3.8 percent of the senior class was college ready.

FDNY HS aims to prepare students for college and careers in EMS or firefighting.

Hollis Moore, 16, an FDNY junior from Queens, said he felt the instruction was good, but that not all of his peers were studious.

“I’m serious about it,” said Moore. “Most of them just play around.”

Another junior, Gregory McMullen, 16, of Queens said the “teachers are great,” but “some kids actually want to do good and some kids don’t.”

The school, one of four housed in the former Thomas Jefferson HS in East New York, admits the shortcomings in its educational plan.

“Despite our successes with graduating students, we still struggle with the amount of students showing significant scoring increases on the Math and English Regents exams,” the plan says. “The area of focus for this issue is going to be rigorous instruction.”

The DOE said the school this year started offering three Advanced Placement classes to better prepare kids for college.

Officials insisted that measures of college readiness, including college enrollment rates, are at record highs. “And we are making unprecedented investments to keep increasing them,” said DOE spokeswoman Devora Kaye.

The DOE lists college readiness rates on annual school “quality snapshot” reports posted on its web site.

Many charter highs also fared poorly, but cited glitches in the data. The New Visions Charter HS for the Humanities in the Bronx had an 86 percent graduation rate with a college readiness rate of 1.2 percent.

A New Visions spokesman said the DOE did not count students who had certain math credits, and its readiness rate is higher than reported — although still far below the city average. The charter network did not notice the lapse until contacted by The Post.

Data analysis by Joshua Tanzer