Drake Equation

The Drake Equation is a formula devised by Frank Drake and used as a focal point for discussion at the Green Bank conference in November 1961. Intended to provide a way of estimating the number of extraterrestrial civilizations in the Galaxy which currently have the ability to engage in interstellar communication (see extraterrestrial intelligence, likelihood), it is written as


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

N Present number of extraterrestrial races capable of interstellar communication
R* Mean rate of star formation, averaged over the lifetime of the Galaxy
fp Fraction of stars that have planets
ne Average number of planets in a planetary system suitable for life
fl Fraction of suitable planets on which life actually develops
fi Fraction of life-bearing planets on which intelligent life develops
fc Fraction of intelligence-bearing planets on which the capacity for interstellar communication develops
L Average lifetime of a technological civilization

Unfortunately, of the seven factors that appear on the right side of the Drake Equation, only one (R*) can be estimated at present with any degree of confidence. Current and near-future research on exoplanets will gradually reduce the uncertainties in three other factors, fp, ne, and fl. However, the values of the remaining three factors, which relate to the evolution of extraterrestrial intelligence and technology, are likely to remain a matter of pure speculation for a very long time, unless contact is made with a more advanced civilization which could convey this knowledge immediately.


Despite the enormous uncertainties involved in using the Drake Equation, which can result in a value of N from less than one to more than a billion, it is at least interesting and instructive to consider each of the factors involved. Aside from Factor 1, the values suggested below are simply the author's own "best guesses".


factor 1: R* (mean rate of star formation)

To a first approximation this is simply the total number of stars in the Galaxy (about 400 billion) divided by the age of the Galaxy (about 10 billion years). That is, R* ~ 40 stars per year.


factor 2: fp (fraction of stars that have planets)

Until recently, this was a matter of pure conjecture since there had been no confirmation of the existence of any planets beyond the solar system. Improved methods of detection, however, led to a flurry of discoveries of exoplanets and protoplanetary disks. This has raised the expectation that planetary systems may be the rule rather than the exception. A conservative estimate might be that one half of all stars in the Galaxy are accompanied by planets. That is, fp ~ 0.5.


factor 3: ne (average number of planets in a planetary system suitable for life)

Here there is considerable uncertainty. It is still not known what constitutes a "typical" planetary system and, in particular, how common it is to have Earth-class planets orbiting within the habitable zone of a host star. Nor is it clear how adaptable life can be to different environments (see extraterrestrial life, variety). The discovery of life on Europa, for example, would increase the number of opportunities for life to have evolved elsewhere. Unless, for some reason, the Solar System is significantly atypical, it might be reasonable to assume that in every two planetary systems there is at least one world capable of sustaining life. That is, ne ~ 0.5.


factor 4: fl (fraction of suitable planets on which life develops)

Again, we are hampered by having knowledge, at present, of only one inhabited world. It may be that some crucial step in the evolution of life is extremely improbable, in which case, even if an environment is biologically clement, life is unlikely to appear. The scientific consensus, however, is presently shifting toward the opposite conclusion; namely, that unless conditions preclude the possibility of life altogether, life is likely to evolve. This view is supported by the discoveries of organic material in space (see interstellar molecules), meteorites, and comets; of water (both liquid and frozen) on worlds other than the Earth; and, most significantly, of extremophiles, which thrive in what, to other organisms, would be extraordinarily hostile environments. The present consensus of astrobiologists suggests that fl ~ 1.


factor 5: fi (fraction of life-bearing worlds on which intelligent life develops)

How often does life in general serve as a precursor to intelligence on a par with or greater than our own? When this issue was raised at the Green Bank conference, John Lilly's claim that intelligence has arisen not once, but twice on this planet (see dolphins, as a form of alien intelligence), encouraged the attendees to adopt a value for fi of 1. As Carl Sagan put it:


[T]he adaptive value of intelligence ... is so great – at least until technical civilizations are developed - that if it is genetically feasible, natural selection seems likely to bring it forth.1


Further evidence for this is the evolution of "brainy" dinosaurs which, had they not become extinct (see Cretaceous-Tertiary Boundary) might conceivably have become the dominant form of intelligence on Earth (see dinosaurs, intelligent). However, it is also possible that some planetary environments, while allowing the emergence of primitive organisms, pose obstacles to higher forms of life. Bearing all these factors in mind, a reasonable estimate might be that fi ~ 0.1.


factor 6: fc (fraction of intelligence-bearing worlds on which capacity for interstellar communication develops)

If the example of dolphins is used to argue the case that emergence of intelligence is common, it must also, in fairness, be used to moderate any estimates of how frequently intelligent life develops the capability for communication over interstellar distances. The existence of large brains, and apparently intelligent behavior, the case of dolphins reveals, is no guarantee of the development of a significant level of technology. For this to happen, a species must possess a high degree of manipulative ability – which, for humans, means having dexterous hands instead of flippers. Perhaps it is a general rule that wherever aquatic (or aerial?) intelligence emerges (see cetaceans; cephalopods), it is non-technological in nature. Intelligence plus technology may only occur among land-dwellers. As in the case of the previous factor, it might be appropriate to adopt a conservative value of fc ~ 0.1.


factor 7: L (average lifetime of a technological civilization)

Of all the factors in the Drake Equation, this is the least well-understood and potentially the most decisive. Various arguments have been brought to bear on the question of how long a typical civilization can be expected to survive, once it has developed the minimum capability to send and receive messages over interstellar distances (see extraterrestrial civilizations, lifetime). Estimates vary between about 100 years, assuming pessimistically that races tend to self-destruct at about the technological level humans have reached today (see extraterrestrial civilizations, hazards to) and several billion years, assuming that once a technological civilization arises it survives as long as its host star. Yet this is only one of the issues involved in assessing a likely value for L, and it is probably not the most significant.


Although in Drake's original formulation, L is taken to be the total lifetime of a technological civilization and N, therefore, the number of civilizations capable of interstellar communication, what is really of concern in assessing the likelihood of success by contemporary SETI programs is the time-span over which a civilization is likely to be trying to communicate over interstellar distances by the kind of technology with which we are familiar today (that is, principally the transmission and reception of radio waves). The important point, which is often overlooked, is that these two quantities may be different by many orders of magnitude. From human experience, it is apparent that once a certain threshold of technological sophistication has been reached, as happened during and immediately after the Industrial Revolution, subsequent progress can be very rapid indeed, and its direction virtually unpredictable. Only an average human lifetime separates the first mechanically-powered human flight by the Wright Brothers from the launch of the first spacecraft to the outer planets. Less than a lifetime separates the first, room-filling programmable computers, such as ENIAC, from present-day laptop computers of vastly greater processing power. The history and pace of technological development suggests that it is unreasonable to suppose that the best means of communication available in one century will necessarily be the best available in the next. What the next breakthrough will be, beyond light-speed, electromagnetic communication, is impossible to say. Perhaps it will involve sending messages outside of normal space-time through microscopic, artificially-constructed wormholes, or exploiting one of the more esoteric consequences of non-locality in quantum mechanics, or using faster-than-light particles (see tachyons) or some other means, such as Morrison's "Q" waves. But it strains credibility to imagine that in the remote (and perhaps not-so-remote) future we shall still be reliant upon radio transmissions and their like for remote signaling. In the same way, it is unreasonable to suppose that a civilization with a technology significantly in advance of our own will be broadcasting messages that are detectable by any of our present-day instruments. A generous estimate might be that there is a 500-yr window during which a technological civilization employs current terrestrial-type methods for communicating over interstellar distances. On either side of that window, it is not likely that we would be aware of the other civilization's presence, just as a dog is unaware of the plethora of electromagnetic signals which surround it on our own planet. Whether or not extraterrestrial technological civilizations survive typically for a thousand years or ten billion years, is not the factor which determines how many races we can hope to make contact with. Providing civilizations typically survive for the few hundred years until they achieve the next quantum jump in communications, this supplies the only value of L that is relevant in the context of our current communications capability. Given these considerations, then, it might be reasonable to assume that L ~ 500 years (with apologies to Walter Sullivan who dedicated his book We Are Not Alone to "those everywhere who seek to make 'L' a large number.").


Inserting these values into the Drake Equation gives


    N = 40 × 0.5 × 0.5 × 1 × 0.1 × 0.1 × 500 = 50.


That is, if these estimates are valid, there are roughly 50 civilizations in the entire Galaxy which are likely to be engaged in trying to communicate using the means presently available to us on Earth. Assuming, as we have, a 500-year "radio-window", and given the fact that humans have had the ability to receive and broadcast interstellar messages for about 50 years, this suggests that there are about 5 radio-capable civilizations that are marginally behind us in their technology and about 45 that are somewhat more advanced yet not sufficiently advanced to have progressed beyond our "earshot". Fifty radio-stage civilizations equates to one for roughly every 8 billion stars. Since the nearest such civilization would probably lie well over 1,000 light-years away, it would not be possible to exchange even a single greeting before one or both of the parties had transcended the proposed 500-yr radio-window.


The ideas discussed here afford one possible explanation of the negative results produced by SETI programs to date. It may be that high intelligence and undreamed-of technology is common in the Galaxy, but that we simply lack the means, at present, to detect its presence.2



1. Shklovskii, I. S., and Sagan, Carl. Intelligent Life in the Universe. New York: Dell (1966).


2. Kreifeldt, J. G. "A Formulation for the Number of Communicative Civilizations in the Galaxy," Icarus, 14, 4190 (1971).


3. Sturrock, Peter A. "Uncertainty Estimates in the Number of Extraterrestrial Civilizations," National Aeronautics and Space Administration, Grant NGR 05-020-668, SUIPR Report No. 808, March 1980; also contained in Strategies for the search for life in the universe; Proceedings of the Meeting, Montreal, Canada, August 15, 16, 1979. (A81-25626 10-88) Dordrecht, D. Reidel Publishing Co., pp. 59-72 (1980).


Abstract: Estimation of the number N of communicative civilizations by means of Drake's formula involves the combination of several quantities, each of which is to some extent uncertain. The uncertainty in any quantity may be represented by a probability distribution function, even if that quantity is itself a probability. The uncertainty of current estimates of N is derived principally from uncertainty in estimates of the lifetime of advanced civilizations. It is argued that this is due primarily to uncertainty concerning the existence of a "Galactic Federation" which is in turn contingent upon uncertainty about whether the limitations of present-day physics are absolute or (in the event that there exists a yet-undiscovered "hyperphysics") transient. It is further argued that it is advantageous to consider explicitly these underlying assumptions in order to compare the probable numbers of civilizations operating radio beacons, permitting radio leakage, dispatching probes for radio surveillance or dispatching vehicles for manned surveillance.