“I’m feeling a little tingly,” he said.

At a news conference Friday discussing the results, astronomers erupted in praise of the Kepler mission and its team. Natalie Batalha, a Kepler leader from the NASA Ames Research Center, described the project and its members as “the best of humanity rising to the occasion.”

According to Mr. Petigura’s new calculation, the fraction of stars with Earth-like planets is 22 percent, plus or minus 8 percent, depending on exactly how you define the habitable zone.

There are several caveats. Although these planets are Earth-size, nobody knows what their masses are and thus whether they are rocky like the Earth, or balls of ice or gas, let alone whether anything can, or does — or ever will — live on them.

There is reason to believe, from recent observations of other worlds, however, that at least some Earth-size planets, if not all of them, are indeed rocky. Last week, two groups of astronomers announced that an Earth-size planet named Kepler 78b that orbits its sun in 8.5 hours has the same density as the Earth, though it is too hot to support life.

“Nature,” as Mr. Petigura put it, “knows how to make rocky Earth-size planets.”

Also, the number is more uncertain than it might have been because Kepler’s pointing system failed before it could complete its prime survey. As a result, Mr. Petigura and his colleagues had to extrapolate from planets slightly larger than Earth and with slightly smaller, tighter orbits. For the purposes of his analysis “Earth-size” was anything from one to two times the diameter of the Earth, and Earth-like orbits were between 400 and 200 days.

Dr. Batalha said, “We don’t yet have any planet candidates that are exact analogues of the Earth in terms of size, orbit or star type.”