This article is about Frank Drake's equation. For the Tub Ring music album, see Drake Equation (album).
The Drake equation (rarely also called the Green Bank equation or the Sagan equation) is a famous result in the speculative fields of exobiology, astrosociobiology and the search for extraterrestrial intelligence.
This equation was devised by Dr Frank Drake (now Professor Emeritus of Astronomy and Astrophysics at the University of California, Santa Cruz) in 1960, in an attempt to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact. The main purpose of the equation is to allow scientists to quantify the uncertainty of the factors which determine the number of such extraterrestrial civilizations.
The Drake equation is closely related to the Fermi paradox.

Historical estimates of the parameters
This section attempts to list best current estimates for the parameters of the Drake equation.
R* = the rate of star creation in our galaxy
Estimated by Drake as 10/year. Latest calculations from NASA and the European Space Agency indicates that the current rate of star formation in our galaxy is about 6 per year..
f_c = the fraction of the above which are willing and able to communicate
Estimated by Drake as 0.01.
L = the expected lifetime of such a civilization for the period that it can communicate across interstellar space.
Estimated by Drake as 10,000 years.
In an article in Scientific American, Michael Shermer estimated L as 420 years, based on compiling the durations of sixty historical civilizations. Using twenty-eight civilizations more recent than the Roman Empire he calculates a figure of 304 years for "modern" civilizations. It could also be argued from Michael Shermer's results that the fall of most of these civilizations was followed by later civilizations which carried on the technologies, so its doubtful that they are separate civilizations in the context of the Drake equation. Furthermore since none could communicate over interstellar space, the value of L here could also be argued to be zero.
The value of L can be estimated from the lifetime of our current civilization from the advent of radio astronomy in 1938 (dated from Grote Reber's parabolic dish radio telescope) to the current date. In 2007, this gives an L of 69 years. However such an assumption would be erroneous. 69 for the value of L would be an artificial minimum based on Earth's broadcasting history to date and would make unlikely the possibility of other civilizations existing. 10,000 for L is still the most popular estimate
Values based on the above estimates,
R* = 6/year, f_p = 0.5, n_e = 2, f_l = 0.33, f_i = 0.01, f_c = 0.01, and L = 10000 years
result in
N = 6 × 0.5 × 2 × 0.33 × 0.01 × 0.01 × 10000 = 2
It is worth noting that the uncertainty in the revised equation is determined primarily by the last 3 factors, f_i, f_c, and L. If any of these are far smaller than assumed above, as some have argued, then the average number of civilizations may be much less than one.

Current estimates of the parameters
Since there exists only one known example of a planet with advanced life forms, some critics view the Drake equation as unreliable. However, based on Earth's experience, some scientists view intelligent life on other planets as possible and the replication of this event elsewhere is at least plausible.. Crichton's criticism might be flawed if extraterrestrial civilizations existed since the negative hypothesis (i.e., "extraterrestrial civilizations do not exist") could be tested: it would be falsified by the discovery of one of them.
It is also noteworthy that actual experiments by SETI scientists do not attempt to address the Drake equations for the existence of extraterrestrial civilizations anywhere in the universe, but are focused on specific, testable hypotheses (i.e., "do extraterrestrial civilizations communicating in the radio spectrum exist near sunlike stars within 50 light years of the Earth?"). These questions are testable (either yes or no).
Some people argue that even though the Drake equation currently involves speculation about parameters that are, as of the moment, unmeasured, it serves a useful purpose by stimulating dialogue between people about these topics, leading to focus and how to proceed experimentally -- and this was Drake's intent in the first place.
One can question why the number of civilizations should be proportional to the star formation rate, though this makes technical sense. (The product of all the terms except L tells how many new communicating civilizations are born each year. Then you multiply by the lifetime to get the expected number. For example, if an average of 0.01 new civilizations are born each year, and they each last 500 years on the average, then on the average 5 will exist at any time.) The original Drake Equation can be extended to a more realistic model, where the equation uses not the number of stars that are forming now, but those that were forming several billion years ago. The alternate formulation, in terms of the number of stars in the galaxy, is easier to explain and understand, but implicitly assumes the star formation rate is constant over the life of the galaxy.

In fiction

Astrosociobiology
Fermi Paradox
Kardashev scale
Sentience Quotient
SETI
Zoo hypothesis