The Drake Equation and Alien Intelligence Calculations Explained

The half-century-old mathematical formula predicting the likelihood of intelligent life is simple and efficient. But it might be time to redo the math.

NASA/CXC/MIT/F. Baganoff, R. Shcherbakov et al.

The Search for Extraterrestrial Intelligence is not just the realm of crackpots and conspiracy theorists. Scientists — especially the really smart ones — are part of the search and have even gone so far as to create an equation to measure the likelihood of that mission’s success.

It’s called the Drake equation. (Get out of here, 6 God, this hasn’t nothing to do with you.)

First designed by astronomer Frank Drake in 1961, the equation tries to take into account all the factors that determine whether humans have the capability to find and communicate with intelligent beings from another world. The formula reads as:

N = R x f(p) x n(e) x f(l) x f(i) x f(c) x L*

There are seven different factors that go into the formula:

  • R* = the rate of formation of stars that would suit the development of intelligent life (i.e. stars similar to the sun)
  • f(p) = fraction of those stars that possess planetary systems or will likely form planetary systems
  • n(e) = the number of planets per star system that have habitable environments
  • f(l) = the fraction of habitable planets that actually have life
  • f(i) = the fraction of life-bearing planets in which that life is intelligent
  • f(c) = the fraction of intelligent civilizations utilizing technology capable of broadcasting their existence into outer space
  • L = the amount of time those intelligent civilizations spend using that technology to broadcast signs of their existence into space.

And when you plug all that in, you’re left with N: the number of civilizations in the galaxy we might be able to communicate with.

When Drake created this equation, he and his colleagues plugged in a set of values for each variable. At minimum, they found N = 20, meaning there were probably 20 civilizations in the galaxy we could communicate with. At a maximum, N comes out to a whopping 50,000,000. That seems a tad high, but hey, they are the scientists…

The point isn’t actually to figure out a real value for N and keep tabs on how many alien worlds we might be able to chat with and invite over for a beer. The Drake equation is just a loose roadmap for neatly piecing together the kinds of things we need to contemplate when we consider the question of whether there is intelligent life elsewhere, whether it is worth investing time and technology into SETI, and what exactly the best methods might be for finding and contacting our future alien overlords. In essence, the Drake equation is more like a statement about what the current state of SETI research is. It acts like a kind of symbol for the curiosity that continues to drive that search.

SETI began as a concerted effort in 1955, with the creation of the Ohio State University SETI program — the world’s first continuous SETI program — and the operation of the “Big Ear” telescope. Since that time, humans have found exactly zero intelligent civilizations originating from other planets.

Despite a half century of absolutely no success, SETI has taken on a renewed interest, thanks in great part to the recent surge of research into identifying and cataloging exoplanets. By extension, many scientists are starting to take another look at the Drake equation, and point out ways in which it could be improved in the context of new research.

One of those modifications is to take into account the potential for alien civilizations to colonize other star systems, using v to express ‘expansion velocity’. This results in a complex set of three different equations — so obviously we don’t have a lot of people throwing their support behind that idea.

The basic chemistry for life has been detected in a second hot gas planet, HD 209458b, depicted in this artist's concept.


A more recent revision was pitched by MIT astronomer Sara Seager. She suggests a modification that would focus the Drake equation on searching for biosignature gases, rather than technological signs of intelligent life. All living organisms — at least the ones we know — produce biogenic gases that rise into the atmosphere and can be detected by space telescopes and other equipment. Her new equation basically specifies that we should be looking for ‘quiet’ stars that have mellowed down from early violent characteristics, rocky planets (providing the necessary support life needs to, you know, standup and stuff), and of course looking for detectable signs of biogenic gas.

In case you haven’t already guessed, Seager’s equation broadens the scope of Drake from searching for intelligent life, to any forms of life. You take the ‘I’ out of SETI, and suddenly you have an endeavor that’s perhaps less exciting, but much more achievable.

A brand new proposed revision of the Drake equation involves actually integrating new exoplanet data in an effort to pinpoint a real value of N. Adam Frank from the University of Rochester and Woody Sullivan at the University of Washington think that instead of trying to determine how many intelligent civilizations might be out there in the great beyond, we should instead ask how many civilizations there have ever been.

In other words: They think a revised Drake equation should show the odds that intelligent life has ever arisen.

This simplifies the Drake equation down by ignoring the need to know star formation rates and the length of time an intelligent civilization has been sending out signs of its technological prowess. When Frank and Sullivan plugged in new data on exoplanets, they found that “as long as the probability that a habitable zone planet develops a technological species is larger than ~10^-24, then humanity is not the only time technological intelligence has evolved,” they write in their paper.

Furthermore, that means, if the probability of an intelligent species evolving on a habitable planet is greater than one in 60 billion, than another intelligent species in the Milky Way probably exists.

You might find those odds favorable, and you might not. Whatever the case, the search will still continue. Like I mentioned before, the Drake equation is simply a discussion point we can use to wrap our heads around the fact that we may or may not be alone in the universe. Anyone — including me — who wants to believe there might be life on another planet will probably respond to any talk about the probability of finding E.T. by quoting Han Solo: “Never tell me the odds.”