The repetition of horror numbs the mind: Only 11 days ago there was Buffalo, with a man driven by racism gunning down 10 people at a supermarket. The next day another angry man walked into a Presbyterian church in Laguna Woods, Calif., and killed one person and wounded five others. And now, Uvalde, Texas — a repeat of what was once thought unfathomable: the killing of at least 19 elementary school children in second, third and fourth grades.

“I guess it’s something in society we know will happen again, over and over,” said Neil Heslin, whose 6-year-old son, Jesse Lewis, died in the Sandy Hook Elementary School shooting in 2012.

The misery mounts, and yet nothing changes, leaving Americans with little more to do than keep lists, mental spreadsheets of death that treat events like Uvalde as just another morbid tally with superlatives like “second-deadliest shooting in an elementary school.”

Each event evokes some atrocity from the past, the exact details of each shooting growing more indistinct by the year: The latest death toll of 21 at Robb Elementary School in Texas surpasses the shooting in Parkland, Fla., in 2018, when 17 people were killed. It falls short of the deadliest school shooting — when 26 people were killed in 2012 at Sandy Hook Elementary in Newtown, Conn.

These are the mathematics of American gun massacres.

All three school shootings — Newtown, Parkland and now Uvalde — have eclipsed Columbine in 1999, when such events still had the power to shock the nation.

The reasons for the violence are familiar and incontrovertible. The United States has many more guns than citizens, about 400 million firearms, according to a 2018 survey conducted by the nonpartisan Small Arms Survey, and 331 million people.

For more than a decade now, semiautomatic handguns, purchased for personal protection, outsell rifles, which have been typically used in hunting.

And the coronavirus pandemic stirred an even greater gun-buying craze. Annual domestic gun production increased from 3.9 million in 2000 to 11.3 million in 2020, according to a report released this month by the Bureau of Alcohol, Tobacco, Firearms and Explosives. A vast majority of those firearms stayed in the United States.

The toll of the violence, especially on children, has only grown. The Centers for Disease Control and Prevention reported that the rate of gun deaths of children 14 and younger rose by roughly 50 percent from the end of 2019 to the end of 2020.

Last year, more than 1,500 children and teenagers younger than 18 were killed in homicides and accidental shootings, compared with about 1,380 in 2020, according to the Gun Violence Archive, a database tracking gun deaths.

Many details about the Uvalde shooting have yet to be made public, including the weapons used by the gunman — an 18-year-old man who died at the scene, the authorities said — and how he obtained them. But the emotional turmoil of the killings was sadly familiar.

“Why are we willing to live with this carnage?” President Biden said on Tuesday night after returning from a trip to Asia. “Why do we keep letting this happen?”

Senator Chris Murphy of Connecticut, a young legislator when the children were killed in Sandy Hook, exhorted his fellow senators to action on Tuesday. “What are we doing? What are we doing?” he said on the Senate floor.

These were questions with typical answers: not much of anything on the federal level. Republicans, often appealing to the Second Amendment, have blocked efforts to add stiffer background checks for gun purchasers every time another major mass shooting jostles the nation’s conscience. Still, within hours of the shooting in Uvalde, Senator Chuck Schumer, Democrat of New York and the majority leader, moved to clear the way to force votes in the coming days on legislation that would strengthen background checks.

In the meantime states like Texas have forged ahead with some of the least-restrictive gun laws in the United States, priding itself as a state with responsible gun owners — more than a million — even with its recent history of mass shootings.

Gov. Greg Abbott signed a wide-ranging law in 2021 that ended the requirement for Texans to obtain a license to carry handguns, allowing virtually anyone over the age of 21 to carry one. The landmark law made the state one of the largest to adopt a “constitutional carry” law that basically eliminates most restrictions on the ability to carry handguns.

Mr. Abbott described it as “the strongest Second Amendment legislation in Texas history.”

Mass shootings have become so common in the United States that only a small fraction rise to attract widespread attention beyond the communities directly affected. On the same weekend as the Buffalo killings, more than a dozen people were wounded by gunfire in downtown Milwaukee, near the arena where an N.B.A. playoff game ended hours earlier, the authorities said.

Two weeks earlier, the owner and two employees of the Broadway Inn Express motel in Biloxi, Miss., were fatally shot, and another person was also shot dead during a carjacking.

Less than four weeks before that, a barrage of gunfire in Sacramento killed six people and wounded 12 in a shooting that the authorities said involved at least five gunmen.

On Monday, the F.B.I. released data showing a rapidly escalating pattern of public shootings in the United States.

The bureau identified 61 “active shooter” attacks in 2021 that killed 103 people and injured 130 others. That was the highest annual total since 2017, when 143 people were killed, and hundreds more were wounded, numbers inflated by the sniper attack on the Las Vegas Strip.

The 2021 total represented a 52 percent increase from the tally of such shootings in 2020, and a 97 percent increase from 2017, according to the F.B.I.’s Active Shooter Incidents in the United States in 2021 report.

In Uvalde, Rey Chapa has a nephew who was at the school during the shooting but was not injured.

“This is just evil,” Mr. Chapa said in an interview, using an expletive. He was waiting to hear back from family and friends about the conditions of other children and scrolling through Facebook for updates. “I’m afraid I’m going to know a lot of these kids that were killed.”

Contributing reporting was Emily Cochrane, Catie Edmondson, Christine Hauser, Eduardo Medina, Sarah Mervosh, Alexandra E. Petri, Michael D. Shear, Glenn Thrush and Elizabeth Williamson.