Are we alone? Fifty-five years ago, astronomer Frank Drake came up with an equation that weighed the odds for aliens, and now two astronomers have tweaked the formula to come up with a slightly different spin.

Their bottom line? There’s an astronomically high chance that other civilizations have arisen elsewhere in the universe at some point in its 13.8 billion-year history.

The University of Washington’s Woody Sullivan and the University of Rochester’s Adam Frank published their assessment in the May issue of Astrobiology, and Frank is following up with an op-ed in Sunday’s New York Times.

“While we do not know if any advanced extraterrestrial civilizations currently exist in our galaxy, we now have enough information that they almost certainly existed at some point in cosmic history,” Frank writes.

He and Sullivan come to that conclusion by deconstructing the Drake Equation. The classic formula starts out with the rate of formation of stars in our Milky Way galaxy, then multiplies that by the fraction of those stars with planetary systems, the average number of habitable planets for each of those systems, the fraction of those planets that give rise to life, the fraction of those life-bearing planets that give rise to civilizations, the fraction of those civilizations that beam out evidence of their existence, and the average length of time during which they’re able to do the beaming. The result tells you how many alien civilizations in the Milky Way you think should be sending out signals.

Simple, right? You can use this interactive to plug in your own estimates and come up with a figure.

The problem is that the latter terms of the equation are squishy, because we just don’t know enough about life beyond Earth to hazard an educated guess. But thanks to the data from NASA’s planet-hunting Kepler space telescope, astronomers are getting a good handle on the first three terms: the number of stars, planetary production and the prevalence of habitable planets.

So Frank and Sullivan focus on what’s known about the big picture, and set aside the time factor.

The Drake Equation, top, combines several factors to come up with an estimate for the number of extraterrestrial civilizations in the Milky Way currently beaming out signals. The Frank-Sullivan Equation, bottom, eliminates the time factors and provides an estimate for the number of advanced cvilizations likely to have developed over the history of the observable universe. Click on the graphic for a larger version. (Credit: University of Rochester)

They start out with an estimate of 20 sextillion stars in the observable universe (2 x 1022). There appears to be at least one planet for every star (1.0). And about one-fifth of those planets appear to orbit in habitable zones (0.2). That gives you a really big number for the estimate of habitable planets in the universe: 4 sextillion, or 4 x 1021.

Then the astronomers add a twist to the equation. How low do you have to set the chances that a habitable planet gives rise to a signal-beaming civilization, in order to reduce what you get when you do the multiplication (planets times probability) to just one world, as in Earth? The number would have to be one chance in 4 sextillion, or 2.5 x 10-22.

“To me, this implies that other intelligent, technology-producing species very likely have evolved before us,” Frank said in a news release about the tweaked equation. “Think of it this way: Before our result you’d be considered a pessimist if you imagined the probability of evolving a civilization on a habitable planet were, say, one in a trillion. But even that guess, one chance in a trillion, implies that what has happened here on Earth with humanity has in fact happened about 10 billion other times over cosmic history!”

Or as Carl Sagan put it in “Contact,” the novel that was made into a movie starring Jodie Foster: “If it’s just us, seems like an awful waste of space.”