Because drug deaths take a long time to certify, the Centers for Disease Control and Prevention will not be able to calculate final numbers until December. The Times compiled estimates for 2016 from hundreds of state health departments and county coroners and medical examiners. Together they represent data from states and counties that accounted for 76 percent of overdose deaths in 2015. They are a first look at the extent of the drug overdose epidemic last year, a detailed accounting of a modern plague.

The initial data points to large increases in drug overdose deaths in states along the East Coast, particularly Maryland, Florida, Pennsylvania and Maine. In Ohio, which filed a lawsuit last week accusing five drug companies of abetting the opioid epidemic, we estimate overdose deaths increased by more than 25 percent in 2016.

“Heroin is the devil’s drug, man. It is,” Cliff Parker said, sitting on a bench in Grace Park in Akron. Mr. Parker, 24, graduated from high school not too far from here, in nearby Copley, where he was a multisport athlete. In his senior year, he was a varsity wrestler and earned a scholarship to the University of Akron. Like his friends and teammates, he started using prescription painkillers at parties. It was fun, he said. By the time it stopped being fun, it was too late. Pills soon turned to heroin, and his life began slipping away from him.

Mr. Parker’s story is familiar in the Akron area. From a distance, it would be easy to paint Akron — “Rubber Capital of the World” — as a stereotypical example of Rust Belt decay. But that’s far from a complete picture. While manufacturing jobs have declined and the recovery from the 2008 recession has been slow, unemployment in Summit County, where Akron sits, is roughly in line with the United States as a whole. The Goodyear factories have been retooled into technology centers for research and polymer science. The city has begun to rebuild. But deaths from drug overdose here have skyrocketed.

In 2016, Summit County had 312 drug deaths, according to Gary Guenther, the county medical examiner’s chief investigator — a 46 percent increase from 2015 and more than triple the 99 cases that went through the medical examiner’s office just two years before. There were so many last year, Mr. Guenther said, that on three separate occasions the county had to request refrigerated trailers to store the bodies because they’d run out of space in the morgue.

It’s not unique to Akron. Coroners’ offices throughout the state are being overwhelmed.

In some Ohio counties, deaths from heroin have virtually disappeared. Instead, the culprit is fentanyl or one of its many analogues. In Montgomery County, home to Dayton, of the 100 drug overdose deaths recorded in January and February, only three people tested positive for heroin; 99 tested positive for fentanyl or an analogue.

Fentanyl isn’t new. But over the past three years, it has been popping up in drug seizures across the country.

Most of the time, it’s sold on the street as heroin, or drug traffickers use it to make cheap counterfeit prescription opioids. Fentanyls are showing up in cocaine as well, contributing to an increase in cocaine-related overdoses.

The most deadly of the fentanyl analogues is carfentanil, an elephant tranquilizer 5,000 times stronger than heroin. An amount smaller than a few grains of salt can be a lethal dose.

“July 5th, 2016 — that’s the day carfentanil hit the streets of Akron,” said Capt. Michael Shearer, the commander of the Narcotics Unit for the Akron Police Department. On that day, 17 people overdosed and one person died in a span of nine hours. Over the next six months, the county medical examiner recorded 140 overdose deaths of people testing positive for carfentanil. Just three years earlier, there were fewer than a hundred drug overdose deaths of any kind for the entire year.

This exponential growth in overdose deaths in 2016 didn't extend to all parts of the country. In some states in the western half of the U.S., our data suggests deaths may have leveled off or even declined. According to Dr. Dan Ciccarone, a professor of family and community medicine at the University of California, San Francisco, and an expert in heroin use in the United States, this geographic variation may reflect a historical divide in the nation’s heroin market between the powdered heroin generally found east of the Mississippi River and the Mexican black tar heroin found to the west.

This divide may have kept deaths down in the West for now, but according to Dr. Ciccarone, there is little evidence of differences in the severity of opioid addiction or heroin use. If drug traffickers begin to shift production and distribution in the West from black tar to powdered heroin in large quantities, fentanyl will most likely come along with it, and deaths will rise.

First responders are finding that, with fentanyl and carfentanil, the overdoses can be so severe that multiple doses of naloxone — the anti-overdose medication that often goes by the brand name Narcan — are needed to pull people out. In Warren County in Ohio, Doyle Burke, the chief investigator at the county coroner’s office, has been watching the number of drug deaths rise as the effectiveness of Narcan falls. “E.M.S. crews are hitting them with 12, 13, 14 hits of Narcan with no effect,” said Mr. Burke, likening a shot of Narcan to “a squirt gun in a house fire.”

Early data from 2017 suggests that drug overdose deaths will continue to rise this year. It’s the only aspect of American health, said Dr. Tom Frieden, the former director of the C.D.C., that is getting significantly worse. Over two million Americans are estimated to be dependent on opioids, and an additional 95 million used prescription painkillers in the past year — more than used tobacco. “This epidemic, it’s got no face,” said Chris Eisele, the president of the Warren County Fire Chiefs’ Association and fire chief of Deerfield Township. The Narcotics Anonymous meetings here are populated by lawyers, accountants, young adults and teenagers who described comfortable middle-class upbringings.

Back in Akron, Mr. Parker has been clean for seven months, though he is still living on the streets. The ground of the park is littered with discarded needles, and many among the homeless here are current or former heroin users. Like most recovering from addiction, Mr. Parker needed several tries to get clean — six, by his count. The severity of opioid withdrawal means users rarely get clean unless they are determined and have treatment readily available. “No one wants their family to find them face down with a needle in their arm,” Mr. Parker said. “But no one stops until they’re ready.”

Our count of drug overdoses for 2016 is an estimate. A precise number of drug overdose deaths will not be available until December.

As the chief of the Mortality Statistics Branch of the National Center for Health Statistics at the C.D.C., Robert Anderson oversees the collection and codification of the nation’s mortality data. He noted that toxicology results, which are necessary to assign a cause of death, can take three to six months or longer. “It’s frustrating, because we really do want to track this stuff,” he said, describing how timely data on cause of death would let public health workers allocate resources in the right places.

To come up with our count, we contacted state health departments in all 50 states, in addition to the District of Columbia, asking for their statistics on drug overdose deaths among residents. In states that didn't have numbers available, we turned to county medical examiners and coroners’ offices. In some cases, partial results were extrapolated through the end of the year to get estimates for 2016.

While noting the difficulty of making predictions, Mr. Anderson reviewed The Times’s estimates and said they seemed reasonable. The overdose death rate reported by the N.C.H.S. provisional estimates for the first half of 2016 would imply a total of 59,779 overdose deaths, if the death rate remains flat through the second half of the year. Based on our reporting, we believe this rate increased.

While the process in each state varies slightly, death certificates are usually first filled out by a coroner, medical examiner or attending physician. These death certificates are then collected by state health departments and sent to the N.C.H.S., which assigns what’s called an ICD-10 code to each death. This code specifies the underlying cause of death, and it’s what determines whether a death is classified as a drug overdose.

Sometimes, the cases are straightforward; other times, it’s not so easy. The people in charge of coding each death — called nosologists — have to differentiate between deaths due to drug overdose and those due to the long-term effects of drug abuse, which get a different code. (There were 2,573 such deaths in 2015.) When alcohol and drugs are both present, they must specify which of the two was the underlying cause. If it’s alcohol, it’s not a “drug overdose” under the commonly used definition. Ideally, every medical examiner, coroner and attending physician would fill out death certificates with perfect consistency, but there are often variations from jurisdiction to jurisdiction that can introduce inconsistencies to the data.

These inconsistencies are part of the reason there is a delay in drug death reporting, and among the reasons we can still only estimate the number of drug overdoses in 2016. Since we compiled our data from state health departments and county coroners and medical examiners directly, the deaths have not yet been assigned ICD-10 codes by the N.C.H.S. — that is, the official underlying cause of death has not yet been categorized. In addition, the mortality data in official statistics focuses on deaths among residents. But county coroners typically count up whichever deaths come through their office, regardless of residency. When there were large discrepancies between the 2015 counts from the C.D.C. and the state or county, we used the percent change from 2015 to calculate our 2016 estimate.

We can say with confidence that drug deaths rose a great deal in 2016, but it is hard to say precisely how many died or in which places drug deaths rose most steeply. Because of the delay associated with toxicology reports and inconsistencies in the reported data, our exact estimate — 62,497 total drug overdose deaths — could vary from the true number by several thousand.