Drake Equation

Some state that by making what they feel are reasonable assumptions and arguments we can ascertain that if life is possible at all, then the universe is so vast that it should not only be possible, but almost certain that there are large numbers of extraterrestrial civilisations in the Universe.

In the early 1960’s Frank Drake sought a way to calculate the probability of finding other intelligent races. He came up with an equation to calculate the possibility of extra terrestrial civilizations; which became known as the ‘Drake Equation’. Drake writes,

‘The basic premise behind the equation is that what happened here will happen with a large fraction of the stars as they are created, one after another, in the Milky Way galaxy and other galaxies. People unfamiliar with the accepted pictures of cosmic and biological evolution might think the equation is highly speculative; in fact, it is just the opposite, since the phenomena it assumes to take place in the Universe are only those we are sure have taken place at least once’ (‘The Drake Equation: A Reappraisal’, pp. 115-18, First Contact).


Here is the equation also known as the Green Bank equation:


N = the number of technological civilizations in our galaxy

R* = The rate of formation of suitable stars

F(p) = the fraction of stars having planets.

N(e) = the number of suitable planets per planetary system.

F(l) = the fraction of planets on which life develops

F(i) = the fraction of life that evolves to intelligence beings.

F(c) = the fraction of intelligent species to develop the means of communication.

L = The length of time such civilizations release detectable signals into space.

Drake and other early extraterrestrial-life enthusiasts, including Carl Sagan, arrived at a value for N between 100,000 and 1,000,000–still only about one technological civilization per million stars in the Milky Way, which astronomers believe contains some 200 billion stars.

Drake equation parameters

Considerable disagreement on the values of most of these parameters exists, but the values used by Drake and his colleagues in 1961 are:

  • R* = 10/year (10 stars formed per year, on the average over the life of the galaxy)
  • fp = 0.5 (half of all stars formed will have planets)
  • ne = 2 (stars with planets will have 2 planets capable of developing life)
  • fl = 1 (100% of these planets will develop life)
  • fi = 0.01 (1% of which will be intelligent life)
  • fc = 0.01 (1% of which will be able to communicate)
  • L = 10,000 years (which will last 10,000 years)

The value of R* is the least disputed. fp is more uncertain, but is still much firmer than the values following. Confidence in ne was once higher, but the discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the creation of their stellar systems. In addition, most stars in our galaxy are red dwarfs, which have little of the ultraviolet radiation that has contributed to the evolution of life on Earth. Instead they flare violently, mostly in X-rays – a property not conducive to life as we know it (simulations also suggest that these bursts erode planetary atmospheres). The possibility of life on moons of gas giants such as Europa adds further uncertainty to this figure.

What evidence is currently visible to humanity suggests that fl is very high; life on Earth appears to have begun almost immediately after conditions arrived in which it was possible, suggesting that abiogenesis is relatively “easy” once conditions are right. But this evidence is limited in scope, and so this term remains in considerable dispute. One piece of data which would have major impact on this term is the controversy over whether there is evidence of life on Mars. The conclusion that life on Mars developed independently from life on Earth would argue for a high value for this term. In 2002, Charles H. Lineweaver and Tamara M. Davis (at the University of New South Wales and the Australian Centre for Astrobiology) estimated fl as > 0.33 using a statistical argument based on the length of time life took to evolve on Earth.

fi, fc, and L are obviously little more than guesses. fi has been impacted by discoveries that the solar system’s orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for hundreds of millions of years (evading radiation from novae). Also, Earth’s very large, unusual moon appears to aid retention of hydrogen by breaking up the crust, inducing a magnetosphere by tidal heating and stirring, and stabilizing the planet’s axis of rotation. In addition while it appears that life developed soon after the formation of Earth, the Cambrian explosion in which a large variety of multicellular life forms came into being occurred considerable amounts of time after the formation of Earth, which suggests the possibility that special conditions were necessary for this to occur.

The well-known astronomer Carl Sagan speculated that all of the terms except for the lifetime of a civilization are relatively high, and the determining factor in whether there are large or small numbers of civilizations in the universe is the civilization lifetime, or in other words the ability of technological civilizations to avoid self-destruction. In Sagan’s case, the Drake equation has been a strong motivating factor for his interest in environmental issues and his efforts to warn against the dangers of nuclear warfare. A lower bound on 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 2004, this gives a lower bound on L of 66 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. Note, however, that the fall of most of these civilizations did not destroy their technology, and they were succeeded by later civilizations which carried on those technologies, so Shermer’s estimates should be regarded as pessimistic.

Some computations of the Drake equation, given different assumptions:

R* = 10/year, fp = 0.5, ne = 2, fl = 1, fi = fc = 0.01, and L = 50 years N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 50 = 0.05

Alternatively, making some more optimistic assumptions, and assuming that 10% of civilisations become willing and able to communicate, and then spread through their local star systems for 100,000 years (a very short period in geologic time):

R* = 20/year, fp = 0.1, ne = 0.5, fl = 1, fi = 0.5, fc = 0.1, and L = 100,000 years N = 20 × 0.1 × 0.5 × 1 × 0.5 × 0.1 × 100000 = 5000

The remarkable thing about the Drake equation is that by plugging in apparently fairly plausible values for each of the parameters above, the resultant expectant value of N is generally often >> 1. However, this conflicts with the currently observed value of N = 1, namely ourselves. This conflict is often called the Fermi paradox. However those people who adhere to the premise of the Fermi Paradox believe that, due to a lack of evidence to the contrary, in all probability, humans (as a technologically advanced species) are effectively alone in at least our part of the Milky Way Galaxy. They further say that since we cannot yet determine the variables of the Drake Equation with any real confidence, we cannot determine the numbers of extraterrestrial civilizations based solely on this equation. We must therefore, they argue, rely on data collection – which is only now beginning to be collected in a significant manner. Only then can we even begin to presume what the values of each of the variables in the Drake equation are, they say.