Fermi and the Drake Equation

The Drake Equation (University of Rochester)

Welcome back! To recap, this series is dedicated to answering questions about the Fermi Paradox — i.e., “where haven’t we heard from (or found) any aliens yet?!” For the second installment, I wanted to address what I feel is the logical next step after asking that question. What are the odds that any are even out there? And, equally important, would we be able to talk to them?

To be clear, until we actually find evidence of extraterrestrial intelligence (ETI) out there, all we have is conjecture and academic exercises. In short, we can only make (semi-) educated guesses as to whether or not any exist and whether there a first-contact situation would ever be possible. Luckily, scientists have been doing this for decades as part of the larger field known as the Search for Extraterrestrial Intelligence (SETI).

This is where the Drake Equation — named for astronomer Dr. Frank D. Drake — comes into play. Introduced in 1961, this equation estimates the number of possible civilizations that could be out there based on a number of parameters. Do not be mistaken. This is not some kind of “alien civilization calculator” (you’ll find that here). Instead, it was a thought experiment Drake presented to his colleagues in order to frame the challenges of SETI research.

Gotta’ Love the Drake!

During the 1950s, the idea of using radio telescopes to listen for extraterrestrial signals was becoming all the rage. The idea itself had been suggested during the late 19th century, but no attempts had been made other than Nikola Tesla’s attempt to listen for signals from Mars. But by the latter half of the 20th century, thanks in large part to the dawn of the “Space Age,” SETI began in earnest.

Green Bank Observatory (NRAO)

Beyond scientific curiosity, the political climate of the Cold War was an added source of motivation for this research. The Soviet Union and the United States (as well as their respective allies) recognized the potential for scientific advancements and even felt there would be an advantage to being the first to make contact with an extraterrestrial civilization.

A pioneering fellow in the field was radio astronomer Frank D. Drake who earned his Ph.D. in Astronomy at Harvard and a B.A. in Engineering Physics from Cornell. In 1959, Drake led the first systematic survey at the National Radio Astronomy Observatory in Green Bank, West Virginia. Known as Project Ozma, the survey used the observatory’s 25-meter (82 ft) dish to monitor the nearby stars Epsilon Eridani and Tau Ceti (which are similar to our Sun) in the ultra-high frequency range (UHF).

The survey lasted between April and July of 1960. While no discernible radio signals were detected, it captured the interest of the scientific community. Along with his famed colleague, Carl Sagan, Drake would become a fixture of the astronomical community and his theories continue to influence the field of SETI to this day.

An Equation for Estimating ETI

In 1961, Drake arranged for a meeting to take place at the Green Bank facility for scientists who were interesting in SETI. All those in attendance were given a chance to discuss SETI research and the possibility of future surveys. While small, the meeting was unprecedented and brought together some of the greatest scientific minds in the world (including Carl Sagan).

As Drake fondly related in a 2016 interview with Science Friday:

“I invited everyone in the world I knew about who was interested in the subject or who had written something about it — so all 12. All [were] very enthusiastic, because they’d all been in a situation I’d been in — that they were very interested in this subject, but it was taboo. They really couldn’t pursue or even talk about it, so it was just a joy to be with other people who were as eager as they were.”

Frank Drake with his Drake Equation (Frank Drake)

In preparation for the meeting, Drake prepared an equation that summed up the scientific parameters SETI researchers were dealing with. As Dr. Drake would later say about the famous equation that would come to bear his name:

“As I planned the meeting, I realized a few day[s] ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it’s going to be to detect extraterrestrial life. And looking at them it became pretty evident that if you multiplied all these together, you got a number, N, which is the number of detectable civilizations in our galaxy. This was aimed at the radio search, and not to search for primordial or primitive life forms.”

The meeting, which included such big-name astrophysicists as Carl Sagan, is commemorated with a plaque that is still in the hall of the Green Bank Observatory today. Mathematically, the Drake Equation is expressed as follows:

N = R* x fp x ne x fl x fi x fc x L

  • N is the number of civilizations in our galaxy we could communicate with
  • R* is the average rate of star formation in our galaxy
  • fp is the fraction of those stars which have planets
  • ne is the number of planets that can actually support life
  • fl is the number of planets that will develop life
  • fi is the number of planets that will develop intelligent life
  • fc is the number of civilizations that will develop advanced technology
  • L is the length of time a civilization has to transmit its signals into space


Values and Uncertainties

As you probably guessed already, the Drake Equation contains a lot of values that are subject to uncertainty. For instance, no one can say with any confidence what the odds are that a potentially-habitable planet will actually develop life, or how often life will beget intelligence (let alone technologically-advanced ones), or how long civilizations are likely to endure before they collapse (or go extinct).

As long as we’re being honest, we might as well admit that the very word “intelligence” is subject to uncertainty. After all, homo sapiens are hardly the only species on Earth that demonstrates an aptitude for learning, reasoning, or tool use. We are, however, the only species (hominid or otherwise) that has progressed to the point where our evolution and development (evo-devo) are bound up with technological dependency.

So even after sixty years, the Drake Equation is subject to a lot of assumptions and guesswork. However, there have been some improvements since the 1960s that have allowed astronomers to place better constraints on these values, or at least to make better-informed estimates.

For example, astronomers today estimate that there are 200–400 billion stars within our Milky Way and that between 1.65 ± 0.19 and 3 new stars form every year. Since there are as many as 2 trillion galaxies in the observable Universe (and assuming that our galaxy represents the norm), that means there could be as many as 1.5–6 trillion new stars forming every year!

Another big development is the way research into extrasolar planets has exploded in the past two decades. Thanks to missions like the Kepler Space Telescope, astronomers have confirmed 4,364 exoplanets in 3,231 systems, with another 5,797 candidates awaiting confirmation. From this, astronomers have made informed estimates on how many planets there are in our galaxy.

Classes of stars and their respective HZs (NASA/ESA/Z. Levy (STScI))

Currently, it is estimated that the Milky Way contains 100 billion planets, which works out to about 50% of its stars having a planet of their own. Furthermore, stars that have multiple planets orbiting them will likely have one or two that orbits within their habitable zone (aka. “Goldilocks Zone”) — where conditions are warm enough that liquid water can exist on the planets’ surfaces.

In fact, based on Kepler data, a team of research scientists recently estimated that there could be as many as 300 million habitable planets in the Milky Way alone. While we can’t know how many of those planets are likely to have life on them at any given time, those numbers present us with some pretty good odds. Ultimately, this may be the most important takeaway from the Drake Equation.

Good Odds!

Since it was first introduced, one of the most obvious consequences of the Drake Equation has been how — even with very conservative estimates for every parameter — it indicates that the odds are good that there are a few advanced species out there that we could communicate with. Check it out:

  • Start with N, which is what the rest of the parameters multiplied will yield
  • Next, factor in a conservative rate of star formation (1.46/year)
  • Assume that only 50% of these stars will have planets (0.5)
  • Factor in the number of planets capable of supporting life (300 million)
  • Factor in a 1% estimate for every remaining parameter but the last (fl, fi, fc)
  • Assume a civilization has 200 years to communicate (that’s modest)

Mathematically, that is expressed as 1.46 x 0.5 x 300 million x 0.01 x 0.01 x 0.01 x 200. What does that yield? 319,740! That means that if only 1% of all the habitable planets in our galaxy will develop life, 1% of those produce intelligent life, 1% of those develop technology, and they only have 200 years with which to send signals (before going extinct, transcending, etc.) that there are over 300,000 species we could be hearing from!

Artist’s impression of Proxima b, the closest exoplanet to the Solar System (ESO/M. Kornmesser)

Suppose we were to be even more conservative, to the point that assuming life is rare (or very rare) in the Universe. Then we would still have a few hundred or a few dozen civilizations in our Milky Way to talk to. I don’t know about you, but I like those odds!

Of course, the actual number of habitable planets in our galaxy is an educated guess, and the values used for the three parameters — fi, fc, and L —are entirely assumed. Without any hard data to go by, there’s no real way to know. Also, this equation and its consequences serve to bring the Fermi Paradox into sharper focus. If the odds are good that even a few dozen advanced civilizations are out there today, why haven’t we found any evidence of them?

Good question, and precisely why the Drake Equation is the second installment in this series! When Fermi asked his famous question (“Where is everybody?”), the existence of ETIs was already considered a statistical likelihood. When Drake formulated his equation 11 years later, nothing had changed as far as the scientific community was concerned.

People still figured that ETIs were a foregone conclusion and that humanity was not alone in the Universe. Alas, not all were convinced, and that is something we will take a look at in the next few installments. Short of assuming there are no ETIs out there or that we’re somehow the only ones who communicate using electromagnetic waves, there must be a reason for this “Great Silence.”

Addition Reading:



Space/astronomy journalist for Universe Today, SF author, and all around family man!

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Matt Williams

Space/astronomy journalist for Universe Today, SF author, and all around family man!