The Drake Equation: What are the odds of finding intelligent life?

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Ever wonder if we’ll find intelligent life in our galazy, with whom we could one day communicate with? With approximately 100 billion stars in our Milky Way, it certainly seems plausible that such a species or civilization might exist.

The Drake Equation, developed by Frank Drake in 1961, is a tool to estimate these odds. The estimates for the variables are rife with debate, but as technology improves, the estimates for each of the variables become more accurate.

The equation is as follows:
The Drake Equation


Where N, the solution, is the number of advanced technological civilizations in the Milky Way galaxy that could communicate with us.

Below are the variables and their estimates. I’ve provided some of today’s “best guesses” but also included my own personal opinion. I’ve provided a link to a tool where you can manipulate the Drake Equation with your own estimates.

N* = The number of stars in the Milky Way galaxy. There’s approximately 100 billion stars in the Milky Way galaxy, and this is more-or-less a good estimate.

fp = The fraction of those stars that have planetary systems around them. Current estimates range from 20% to 50%. Let’s take 50%, because we are detecting more and more planets around stars each year with improved technology, so this seems increasingly likely.

ne = The average number of planets in a given planetary system that are suitable for the development of life. The current estimate is 1 to 5. Let’s take 2 as a low average.

fl = The fraction of those planets where life actually arises. Very wide range here… if we assume that where life can evolve, it will, then it’s 100%. Or we can assume that it’s incredibly difficult for life to start, so close to 0%. Let’s take 10% as low average, since we have not found sufficient evidence to indicate how likely life is to evolve on other planets.

fi = The fraction of those planets with life on which intelligent life appears. Intelligence grants a survival advantage, so we might be able to assume that there’s at least a 10% chance (I’m being pessimistic and halving Dr. Drake’s estimate). But to get to the level of the species home sapiens (at least), the numbers are very small – 1 species out of approximately 50 million (estimates range from 5 million to 100 million species on Earth… but who knows how many species would be on another planet?). Taking 50 million as our number, the fraction is then 0.00000002.

fc = The fraction of those planets with intelligent life that develop a technological civilization capable of communicating to and from their planet. Here, again, the assumption is that an intelligent species will have the desire and means to communicate outside of their planet. Looking back into history books, collectively, it certainly seems that the desire is there. The means – perhaps 10% or less. Say 1% for a low estimate.

fL = The fraction of the life of a planet that a technological planet survives. Using our own Earth as an example, what is the fraction of the Earth’s life where the species is communicating? We’ve been communicating with radio waves (cabable of penetrating into deep space)for less than 100 years of the years 4.7 billion year old history. The “100” extends until our civilization is destroyed or collapses, until we are no longer able to communicate. This is difficult to estimate. For example, if we were destroyed today, the fraction is 1/100,000,000th. If we survive 10,000 years, the answer will be 1/1,000,000th. For this example, I’m going to take 1000 years of survival with the ability to communicate, or 1/10,000,000th.

Plug these numbers into the equation, and you get N = 1. In my head, as a general thought experiment without using the Drake Equation, I would think (and hope) the number would be higher.

Dr. Drake, when he plugs in his estimates, gets N = 10,000

Drake Equation Values

The Reappearance Factor…

Since the inception of the Drake Equation, it has been modified to include another fraction nr. This is defined as “how many times an intelligent civilization may occur on planets where it has happened once”. Even if an intelligent civilization reaches the end of its lifetime after, for example, X years, life may still exist the planet for billions of years, allowing another civilization to evolve. As a result, several civilizations may come and go during the lifespan of one planet. So if nr is the average number of times a new civilization reappears on the same planet where a previous civilization once has appeared and ended, then the total number of civilizations on such a planet would be (1+nr).

Using my calcualtion above, the reappearance factor, for me, is a wild guess – if you assume “3”, then our N = 3. Using today’s modern estimates for the Drake Equation and multiplying by the reappearance factor, the result for N is 2.31.

You can try out your own estimates here:

If we consider the case “how many planets support life”, then the number increases significantly. Using a modified version of the Drake Equation (removing the values fi, fc, fL), we get a value of 20 billion (or 1/5). Add intelligence back into the equation and the number is only 400 (I used our tiny fraction of 0.00000002, which is an estimate of the number of species on Earth that are at least as intelligent as the homo sapiens.

Try out the Drake Equation – what numbers do you get for your estimates? Do you think the that the value for N is high enough to warrant the search for extraterrestrial signals?

If you change the definition of N, so that N = the number of advanced civilizations that could communicate with us in the Universe… then you can multiply by another several billion*.

It’s fun to manipulate the numbers of the Drake Equation, but the concept of life outside of our solar system is far more enticing and exciting. Hopefully, SETI will one day be able to discern a signal from space that will help to answer one of the most difficult questions in science: Are we alone? Looking through the eyes of the Hubble Deep Field, you can’t help but wonder.

*I say “several” because even though there are approximately 100 billion galaxies in the Universe, how many of them are stable enough to support a solar system that can sustain life?