It found that reactor No. 1 at Three Mile Island, near Harrisburg, Pa., would appear to be at greatest risk. (Three Mile Island is, of course, the plant that suffered a partial core meltdown in reactor No. 2 in 1979, the worst accident so far in the commercial nuclear power industry in the United States) By the commission’s calculations, such an episode would occur there roughly once every 2,227 years. By contrast, the expected frequency of a core damage accident at the Quad Cities facility in Illinois is once every 833,000 years.

“These sorts of big numbers can tell you which plants need to take steps first to fix general problems, or which plants might have wider margins if a problem were to occur,” said David Lochbaum, a nuclear engineer and the director of the Nuclear Safety Project of the Union of Concerned Scientists, an environmental and nuclear watchdog group. “They’re not going to tell you when that bad day is going to arrive.”

Regulators and federal courts have discounted the likelihood of multiple crises hitting a nuclear facility at the same time. One federal judge, ruling against opponents of the Diablo Canyon nuclear plant near San Luis Obispo, Calif., said that the odds of an earthquake setting off a nuclear accident at the plant were negligible.

“The commission has determined that the chance of such a bizarre concatenation of events occurring is extremely small,” the court said.

But the crisis at Fukushima shows that such natural catastrophes can occur. The fact that the odds of a nuclear accident are unknowable and the risks hard to measure make it in some ways more frightening than the known — and greater — risks of driving without a seat belt or breathing the fumes from a coal-burning power plant.

“People are scared of certain things. It’s part of our makeup,” said Robert H. Socolow, a physicist at Princeton University. “The public is more afraid of radiation than the experts who work with it every day. But this is about irreducible irrationality, if you like. We are irrational, every last one of us.”

Fresh Eye on American Plants

In the wake of the disaster in Japan, concerns were quickly raised at the Turkey Point nuclear power plant in Florida, on Biscayne Bay 24 miles south of Miami. Critics pointed to the potential for a hurricane to create a storm surge that could simultaneously sever grid power and inundate backup generators — precisely the recipe that crippled Fukushima.