Let's Solve The Drake Equation - How Rare is Intelligent Life?

We can use radio telescope arrays to search for signals from alien civilizations, but how likely are we to find something?

How likely is it that there are intelligent civilizations out there beyond our Solar System? This is the question that Frank Drake asked in 1961 when he came up with the eponymous Drake Equation. In the search for extraterrestrial life, finding an intelligent civilization that we might even be able to communicate with is the gold standard. We might not have found any yet, but given our knowledge of how the universe works, we should be able to predict how rare or common they are. That’s the purpose of the Drake Equation.

Despite its name, the Drake Equation isn’t actually a quantifiable equation meant to be solved. Instead, it’s a probabilistic argument designed to provoke thought on the topic. Rather than plugging in numbers and getting an exact result, you plug in estimates to get an estimate. As such, no “solution” to the Drake Equation is exact. The estimate you get out is only as good as the estimates you put in.

The Drake Equation is:

N = R_∗ ⋅ f_p ⋅ n_e ⋅ f_l ⋅ f_i ⋅ f_c ⋅ L

Each factor in the equation represents a different aspect important in the development of intelligent life. R_∗ is the average rate of star formation in our galaxy, f_p is the fraction of stars that have planets, n_e is the average number of planets per star that could potentially support life, f_l is the fraction of planets that can support life that end up actually supporting it, f_i is the fraction of planets with life that develop intelligence, f_c is the fraction of intelligent life that develops to the point where they can release detectable signs of their civilization into space, and L is the lifetime of such a civilization. By multiplying all of these factors together, we’ll get N, which is the predicted number of civilizations we could hypothetically detect within our galaxy. Let’s look more closely at each factor and come up with our own prediction.

The Drake Equation and its factors. Image Credit: NOIRLab/AURA/NSF/P. Marenfeld (CC BY 4.0)

Starting at the beginning with R_∗, the average rate of star formation. This one is the easiest and least controversial factor of the Drake Equation. Modern calculations tell us that stars form in our galaxy at a rate of about 1 to 3 per year. Let’s assume an average of 2 stars per year and plug that into our equation.

As for the fraction of stars with planets, f_p, this is going to be a number from 0 to 1, with 0 being there are no planets (which we know to not be true) and 1 being all stars have planets. We’ve gotten pretty good at finding exoplanets around other stars, and the more we find, the more it seems that stars have planets as a rule, not an exception. As such, we can estimate f_p as 1.

Now things start to get more controversial. How many planets per solar system can support life? It’s difficult to say. If we look at our Solar System alone, the answer is at least 1. However, all we have is the one example. Making a prediction based on a sample size of one isn’t the best science. On the other hand, life might be even more common than we think, based on our Solar System, after all, even if Mars never supported life, it does exist at the right distance from the Sun to possibly have supported it, bumping the number up to 2. Venus, despite being completely inhospitable, is still in the habitable zone, and could have supported life had it gone down a different planetary evolution path. Then there’s the possibility of life on moons. There’s far more moons than planets in our Solar System. Saturn alone has 292 known moons. Jupiter has another 115. There is a realistic chance that moons such as Enceladus and Europa,  which both contain massive subsurface oceans, could have life as well. That’s as high a number as 4. Let’s be moderate and say 1 planet per star could potentially support life.

But what fraction of those planets, f_l, actually develop life? Well, seeing as life appeared on Earth nearly as soon as it possibly could have, that might imply the answer is near 1 in 1, or 100%. An argument against this idea is that life has only appeared on Earth once. There is only one tree of life that we know of. If it’s easy for life to appear on its own, then why wouldn’t it have happened a second time on Earth? However, it is worth noting that once one type of life exists, it would likely discourage any new form of life from appearing by having the evolutionary advantage and instantly out-competing it. Let’s assume f_l equals 1 for now.

Now we get really controversial with f_i, the fraction of planets with life that develop intelligent life. There are two primary ways of looking at this one. The skeptical way is to point out that of all the billions of species on Earth, only one intelligent species has evolved, implying that only an exceedingly small fraction of life will ever become intelligent. Alternatively, the optimistic way to look at it is that only one intelligent species needs to develop per planet, and so far, we’re one for one on that front. Intelligence could be the ultimate evolutionary advantage, and therefore would arise often on planets supporting life. Let’s assume it’s somewhere in the middle and pick a value of 0.5 for f_i and say that 50% of planets with life eventually develop intelligent life.

But how many intelligent civilizations could we actually detect? After all, we’d have a hard time detecting humanity any time from the 1800s or earlier. For f_c, we want to know what percentage of civilizations could be detected. While humanity isn’t purposefully sending out messages of our presence into the stars, we are doing so accidentally. Since the invention of radio, all of our signals have been leaking out into space and working their way deeper and deeper into the galaxy. It seems natural to think that any intelligent species would eventually develop radio communication of their own and begin to broadcast themselves, whether by accident or on purpose. As such, we can estimate f_c at 1.

Of all the factors, L, the average lifetime of an intelligent civilization broadcasting their existence, is perhaps the most important to the Drake Equation. On the low end, looking at human history as an example, civilizations on Earth tend to last about 400 years on average. But those civilizations weren’t the kind we’d be looking for. An argument could be made that once a civilization develops the ability to travel into space, it has gained the ability to allow itself to exist for billions of years, if not indefinitely. If so, that would drastically increase the odds of finding another intelligent civilization. Let’s set L at a thousand years. That’s a nice long time, without assuming all civilizations will last forever.

We now have all our factors, and our equation looks like:

N = 2 ⋅ 1 ⋅ 1 ⋅ 1 ⋅ 0.5 ⋅ 1 ⋅ 1000

This math is actually pretty easy. With all our middle of the road estimates, we would be looking at upwards of 1000 civilizations across the Milky Way galaxy right now. If we instead used all optimistic, but still realistic, numbers, we could get that estimate up to 15 million. Alternatively, using the more reserved, but not entirely pessimistic, numbers would give somewhere around 3 to 5 civilizations.

It’s also worth noting that this is only for the Milky Way galaxy alone. Given that we can see 2 trillion galaxies in the visible universe, even the lower estimates still suggest there could be trillions of civilizations in the observable universe.

This is all, of course, nothing but an estimate. We don't have definite answers for most of this. But, given the fact that a realistic estimate, using realistic scientific evidence could relatively easily give thousands, if not millions of civilizations in our galaxy alone, perhaps we’re really not alone after all.