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Considering the Drake Equation

For most of our history, thinkers have speculated about whether intelligent life existed on other worlds. A common thread runs through their concepts: the vastness of space hides worlds un-numbered, and such a multitude of bodies must have brought forth creatures much like humans.

The advancement of science gave substance to these visions. But it was only in the middle of the last century that we could begin to do more than speculate about possibilities for intelligent extraterrestrial life. It was Frank Drake who, in 1961, took the first step, setting the intuitive answer on a firmer foundation. He linked a series of probabilistic factors into an equation that now bears his name, and used it to estimate the number of intelligent, technical, communicative civilizations that might be extant in our galaxy, the Milky Way. Later, working with Carl Sagan, he modified it into a more useful form.

The original form of the equation started with R*, the rate of formation per year of suitable stars in the galaxy, and ended with L, the number of years during which a civilization remains communicative. You'll notice that the "years" cancel out, giving a pure number. In the modern form, these two factors have been replaced; the other five remain unchanged.

(You can compare the forms. The SETI Institute site shows the original form, while Bradley Keyes has a page giving the modern form. Both of these pages offer an on-line calculator for "N"; here is the SETI Institute's Drake Equation calculator.)


To me, the modern form of the Drake Equation seems easier to understand. It is

[Eq. 1]
N = N* × fp × ne × fv × fi × fc × fL


N* = Estimated number of stars in the Milky Way Galaxy (Factor 1)
fp = Estimated fraction of stars that have planets (Factor 2)
ne = Estimated number of planets per star that could sustain life (Factor 3)
fv = Estimated fraction of suitable planets where life does evolve (Factor 4)
(that is, viviparous, life-bearing — stretching the definition of viviparous a bit)
fi = Estimated fraction of life-bearing planets where intelligent life evolves (Factor 5)
fc = Estimated fraction of intelligent life that communicates across interstellar space (Factor 6)
fL = Estimated fraction of the planet's life during which the communicating civilization lives (Factor 7)

As noted, all of these numbers are estimates. When all of them are multiplied together, we come up with: N, the number of communicating civilizations in the galaxy.

Let's examine these seven estimated factors one by one.

Factor 1

The number of stars in the Milky Way is estimated at between 200 billion and 400 billion. This is based on surveys of the number of stars we can see per unit volume of space, multiplied by the total estimated volume of the galaxy. It is a rather shaky estimate, since so much of the galactic core is hidden by clouds of gas and dust. It is a usable number. However, there are complications that the modern form of the Drake Equation does not recognize. Not all of those stars, according to current theories, can ever have life-bearing planets. Some, while possessing planets, simply pass away too quickly for life to arise on them. Others are part of multiple-star systems, where the clash and tug of conflicting gravitational fields will either prevent planets from forming, or keep them from settling into suitable orbits. Recall that the term in Drake's original form was the rate of suitable star formation.

I choose the higher number, 400 million, for my value of Factor 1.

Factor 2

The fraction of those stars around which planets form is currently being revised upward, thanks to the work of several teams of astronomers. A standard estimate for this number is 20%. Frank Drake endorses it. So will I.

Those discoveries of extrasolar planets affect this estimate as well. So do recent findings in our own solar system, notably the likelihood of a water ocean on Jupiter's moon Europa. All things considered, we may have to set this estimate at 3 to 5; but for now I'll be conservative and leave it at 1.

Factor 3

Here we enter the realm of pure guesswork. What we know about biology suggests that, where planets with the right raw materials exist in stable orbits, life will arise. But, so far, this can be only a suggestion. I'll pick another conservative number out of the air: 10%.

Factor 4

How often does life become intelligent? Again, we can only guess. I'll pessimistically propose an estimate of 0.1%.

Scientist William Calvin has a lot to say about why one form (humans) became intelligent. He's been researching the question for years, and has written several books about it. Some of his writing is available on the Web; see the links below.

Factor 5

If life becomes intelligent, how often does it develop technology? According to our current understanding, this depends first on morphology (body form) and second on environment.

Morphology comes into play as the primary enabler for technology development because technology means the manipulation of matter. To put it simply, if a species doesn't grow hands (or tentacles, or other appendages capable of grasping solid objects), it won't be able to throw stones, much less fashion them into arrowheads and other artifacts.

If a species, however intelligent, lives in water (and especially sea water, which conducts electricity), it seems destined never to develop several of the inventions upon which our technology is founded: fire, electric power, machines that fly in the air, certain aspects of chemistry. Thus environment, too, strongly influences the inherent ability of any species to develop technology.

Personally, I tend to give life more credit for "ingenuity" in this area. My thinking draws a parallel with our own history. We don't have wings — yet we fly. We cannot emit pulses of sound like bats, or pulses of light like fireflies — yet we have sonar as well as radar, we fill our houses with light at night, and we use both light and radio for long-distance communication.

Since the whole subject must rely on speculation, let me speculate about this. If an intelligent, marine species cannot have hearth-fires, might they not develop another way of warming their immediate surroundings? Some chemical reaction might serve. Of course, living in such a constant-temperature environment, they might not need to produce extra heat for personal comfort. But that begs the question of industrial thermal processing, such as casting metals. Consider: animals have evolved ways of making very complex shapes. They do it the old-fashioned way, one molecule at a time. Many species produce bone; some produce rock-hard shells from chemicals dissolved in sea water. Is it really so hard to believe that life elsewhere might have evolved the trick of making metal objects this way? And if life can do this by nature, why cannot intelligence do it to order? (We humans call this method "nanotechnology", and we are beginning to achieve some success at it.) As for underwater electricity, consider the shark's method of detecting prey; consider the electric eel.

The question of grasping members seems to me even less of an obstacle. Many species on this planet have them. A few examples: humans, apes and monkeys all have opposable thumbs; raccoons and other mammals dip food in water to wash it; octupuses and squid have tentacles with suckers. And many insects and spiders can manipulate their prey at least enough to hold it while chowing down.

This could be a long discussion. I'll end it here, and arbitrarily assign a value of 10% to this factor.

Factor 6

Given a technological species: How often does it use that technology for interstellar signalling? This could lead to really lengthy speculations. I'll just say that Factor 6 is 10%.

Factor 7

And the last factor is the biggest question mark of them all. Here, I choose to be somewhat optimistic. I'll say that the communicative lifetime of a civilization is 100,000 years. Taking the average time of habitability of a planet as 4 billion years makes Factor 7 become 0.0025%.

Multiply these seven factors together, and the answer you get is 200 — a not insignificant number of members for the hypothetical Galactic Federation! Now consider that many of the values I chose are quite pessimistic. For example, pegging the percentage of a planet's habitable span when it harbors a communicative civilization at 0.0025% (communicative lifetime of 100,000 years) is not really all that optimistic. We started using stone tools a lot longer ago than that. In fact, only slightly more favorable numbers in a few of the other factors will raise the estimated number of talkative worlds considerably. It's still a game of numbers — and speculation — and hope.


  1. Bradley Keyes' Active Minds page
    Note: has pop-up ads.
  2. SETI Institute's background page for the Drake Equation
  3. The Extrasolar Planetary Foundation's writeup
    Approved by Frank Drake
  4. The SETI League's page
  5. Beyond the Drake Equation
    Douglas Jones' long and rambling — but intelligent — page.
    Includes applets to calculate user-supplied values.
  6. Michael Meyer, NASA senior scientist for astrobiology, leads a 5-part debate about Peter Ward and Donald Brownlee's book Rare Earth.
    Slow to load, but worth the wait


  1. "The Emergence of Intelligence"
    © Scientific American Presents, 1998 (PDF)
  2. "Pumping up Intelligence"
    Calvin's chapter in The Evolution of Intelligence (1999)

Above links verified 5/15/2005.

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