Even self-inflicted shootings that are clearly accidental, like that of Lucas Heagren in Ohio, can wind up classified as homicides.

Lucas’s father, Joshua Heagren, had tried to teach the 3-year-old to respect firearms. The boy had gotten a .22 rifle for Christmas, and his father showed him how to fire it. But he also warned him to handle it only when an adult was present.

“He never even attempted to touch guns when Josh wasn’t around,” Lucas’s mother, Kaitlin Campbell, testified at Mr. Heagren’s trial, where he was convicted of negligent homicide and endangering children. “He knew.”

On the day of the accident, Mr. Heagren had been planning to go out shooting, so he took his pistol from the bedroom, where he normally kept it in a holster between the mattress and the box spring, according to his court testimony. When Ms. Campbell and Lucas returned from buying an inflatable swimming pool, Mr. Heagren slid his gun under the couch before heading outside to set up the pool.

At some point, with his mother distracted by her phone a few steps away, Lucas discovered the gun, grabbed the butt and squeezed the trigger with his thumbs, according to the authorities.

“Our thought process was, parents have a duty to keep their child safe,” said Dr. Lisa Kohler, the Summit County medical examiner, whose office classified the case as a homicide. “Leaving a loaded weapon in an area where the child can easily access it is neglect in our mind. Therefore parents have failed to keep a child safe, and therefore it’s a homicide.”

Dr. Kohler said that because of the neglect issue, her office would almost never classify a firearm-related death as accidental, but added, “Different jurisdictions are going to handle things differently.”

Bob Anderson, the chief of the mortality statistics branch at the National Center for Health Statistics, explained that the federal data on firearm deaths are “only as good as the information that comes in.”

“I try to tell people when they look at the accidental data, particularly for children, you have to recognize it’s an underestimate,” he said.

A few public health researchers have noted the undercount in the past, based on their own academic studies. (One study found the opposite phenomenon — an overcount — among fatal gun accidents involving adults because of a different quirk in the data.) To get more accurate information about firearm deaths, researchers have pushed for the expansion of the National Violent Death Reporting System.

The effort first started in the 1990s at the C.D.C. but was shut down shortly afterward when Congress, at the urging of the N.R.A., blocked firearms-related research at the centers. The project was revived in 2002 after researchers decided to expand its scope beyond guns, but it is up and running in only 18 states. President Obama has called for increased financing for the program, part of a package of gun-related proposals made after the school shooting in Newtown, Conn., last December.

Another important aspect of firearm accidents is that a vast majority of victims do not die. Tracking these injuries nationally, however, is arguably just as problematic as tallying fatalities, according to public health researchers. In fact, national figures often cited from the Centers for Disease Control and Prevention’s Web site are an estimate, projected from a sampling taken from hospital emergency departments. Nevertheless, in 2011, the most recent year with available data, the agency estimated that there were 847 unintentional nonfatal firearm injuries among children 14 and under.

More concrete are actual counts of emergency department visits, which are available in a small number of states. In North Carolina, for instance, there were more than 120 such visits for nonfatal gun accidents among children 17 and under in 2010, the most recent year for which data is available.

Image Noah McGuire, 14, was shot by a friend who thought the gun was unloaded.

A Failed Lock

On a hot and humid August afternoon last year in Hinesville, Ga., Matthew Underhill, a staff sergeant in the Army, was mowing the lawn while his wife, Tessa, was in the house watching television with their 5-year-old son, Matthew. Their other son, Tristan, 2, was scampering down a hallway toward the bedrooms.

It had been a good day for Tristan. He had used the potty for the first time. He and his mother had danced a little jig. Down the hall, Tristan entered the bedroom where his father had been staying because of quarrels with his wife. She had chided her husband in the past for forgetting to safely store his .45-caliber handgun. But he had recently put a lock on his door to keep out his wife and children. He thought he had locked the door before going out to cut the grass.

The lock, though, had failed to catch. Tristan found the loaded gun under the pillow on his father’s bed. He pointed it at his own forehead and pulled the trigger. Hearing the gunshot, Sergeant Underhill sprinted inside to find Tristan face down on the bed, the gun beneath him. When he called 911, the sergeant was screaming so hysterically that the dispatcher initially mistook him for a woman.

“My 2-year-old just shot himself in the head,” he said breathlessly. “He’s dead.”

Tristan’s death underscored several themes running through the cases examined by The Times.

While about 60 percent of the accidental firearm deaths identified by The Times involved handguns as opposed to long guns, that number was much higher — more than 85 percent — when the victims were very young, under the age of 6. In fact, the average handgun victim was several years younger than long gun victims: between 7 and 8, compared with almost 11.

Over all, the largest number of deaths came at the upper end of the age range, with ages 13 and 14 being most common — not necessarily surprising, given that parents generally allow adolescents greater access to guns. But the third-most common age was 3 (tied with 12), a particularly vulnerable age, when children are curious and old enough to manipulate a firearm but ignorant of the dangers.

About a quarter of the victims shot themselves, with younger children again especially susceptible. More than half of the self-inflicted shootings involved children 5 or under; the most common age was 3.

About half of the accidents took place inside the child’s home. A third, however, occurred at the house of a friend or a relative, pointing to a potential vulnerability if safe-storage laws apply only to households with children, as in North Carolina.

In opposing safe-storage laws, some gun rights advocates have argued that a majority of accidental shootings of children are committed by adults with criminal backgrounds. The Times’s review found that was not the case — children were most often the shooters — and that the families involved came from all walks of life.

On Dec. 1, 2006, Beth Dwyer was getting her two boys, ages 5 and 8, ready for school. Her husband, Daron, the minister of music at the family’s church in Gastonia, N.C., was not home because he had enrolled in a seminary several hours away. The night before, Ms. Dwyer had taken the family’s .25-caliber handgun from the top drawer of a dresser and placed it next to her on the bed. In the morning, she forgot to put it away.

Her 8-year-old found the gun. He initially tried to cock it and pulled the trigger, pointing the gun at the bathroom floor, but nothing happened, according to the medical examiner’s report. Evidently thinking the gun was empty, he tried again, pointing the gun at his brother, Matthew, who was crouched on the bathroom counter, having just finished brushing his teeth. This time, with a live round in the chamber, the gun went off, and Matthew toppled to the floor, shot through the forehead.

Even in accidental shootings where criminals were in some way involved, they usually were not the ones pulling the trigger. Rather, they — like many law-abiding adults in these cases — simply left a gun unsecured.

As a felon, Anthony Wise was not supposed to have a firearm. But he was able to buy a .38 Special revolver on the street for $30. He had it in his ex-girlfriend’s apartment in Venice, Ill., on Jan. 29, 2007, when he left it next to a computer in the living room and went to another room. Within minutes, a 4-year-old boy, one of several small children in the apartment, picked up the gun and pointed it at his 2-year-old cousin, Timberlyn Terrell. The gun fired. The boy later told an investigator what happened next.

Image Matthew Dwyer, 5, was shot by his brother with a pistol his mother had left out.

“Blood came out of her forehead,” the boy said, according to a transcript of the interview. He then said he did not want to talk about it anymore and asked for “my mama.”

Timberlyn died. Mr. Wise was convicted of felony firearm possession, but his 10-year federal prison sentence was based in part on the judge’s determination that he had also endangered a child with his negligence.

“Wise would have been a felon in possession even had he possessed the gun in a more responsible way — say, if he had kept it unloaded in a locked cabinet, or if he had kept it unloaded with a trigger lock,” an appellate judge wrote in rejecting his bid for leniency. “More than likely, though, responsible possession would not have endangered the lives of children.”

Safety vs. Self-Defense

The impact of the undercount of accidental gun deaths emerges in stark relief in the statehouse battles over gun-storage laws.

In state after state and often with considerable success, gun rights groups have cited the federal numbers as proof that the problem is nearly inconsequential and that storage laws are unnecessary. Gun Owners of America says on its Web site that children are “130 percent more likely to die from choking on their dinner” than from accidental shootings.

In February 2012, the rifle association issued a member alert about a proposed safe-storage law in Washington State, arguing that shootings are “at the bottom of the list of causes of accidental harm to children.” The group accused State Senator Adam Kline, who introduced the measure, of being interested only in “making life miserable for law-abiding gun owners.” The legislation never made it out of committee.

Under the Centers for Disease Control and Prevention figures, in fact, gun accidents were the ninth-leading cause of unintentional deaths among children ages 1 to 14 in 2010. (The agency reported 62 such killings that year.) If the actual numbers are, in fact, roughly double, however, gun accidents would rise into the top five or six.

Gun rights groups have certainly called on gun owners to safely store their firearms. The National Shooting Sports Foundation says that it has distributed 36 million free firearm safety kits and that manufacturers have shipped 60 million locks with guns sold since 1998. But the groups argue that requiring gun owners to lock up their weapons could make it harder to use them for self-protection.

The rifle association and its allies also often note that studies on the impact of safe-storage laws have found mixed results. But those studies are based on the flawed government statistics.

“When we’re evaluating child access laws, we’re using total trash data,” said Catherine Barber, a researcher at the Injury Control Research Center of the Harvard School of Public Health.

Getting a definitive count of the number of states with a safe-storage law is difficult, but The Times identified only 18, using information from the Law Center to Prevent Gun Violence and researchers who have studied the laws. And in most of those states, charges can be brought only if the child uses the weapon in a threatening manner, injures someone with it or displays it in public.

Even so, in one state, North Carolina, where the law is narrowly drawn to apply only to adults with minors living at home, the authorities charged about 150 people between June 2006 and June 2011, an analysis of court records shows.

Jodi Sandoval of Ohio discovered the limits of her state’s laws after her 14-year-old son, Noah McGuire, was accidentally killed on July 5, 2012, in a suburb of Columbus.