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The Drake Equation

In 1961, Frank Drake wrote a seven-variable equation to estimate how many alien civilisations we could contact. We still don't know the value of a single variable with any certainty.

In plain English

Imagine you want to estimate how many of your neighbours own a cat. You don't know for certain, but you can reason about it: there are about 30 houses on your street, maybe half of them have pets, of those maybe half have cats... you multiply your best guesses together and arrive at a rough estimate. You might be wrong. But you have a number, and a number is more useful than a shrug.

That is what Frank Drake did, but for alien civilisations.

The Drake Equation multiplies a series of estimated quantities together to arrive at N: the number of technologically advanced civilisations in our galaxy that we might currently be able to detect. It was written in 1961, the night before Drake hosted the first scientific conference on the search for extraterrestrial intelligence. He wanted to structure the conversation.

Plug in optimistic numbers and you get millions of civilisations. Plug in pessimistic numbers and you get fewer than one. Both answers come from the same equation.

Five things to file under "wait, what?"

  • Drake scribbled it on a piece of paper the night before a conference. It was not intended to be definitive. It was a way to organise what was unknown. It has since defined a field.

  • The equation has seven variables. The rate of star formation, the fraction of stars with planets, the fraction of planets that could support life, the fraction where life actually develops, the fraction where intelligence develops, the fraction that develops detectable technology, and, the real wildcard, L: how long a civilisation remains detectable before going silent or going extinct.

  • L changes everything. If civilisations survive for millions of years after developing radio technology, N is huge. If they tend to destroy themselves within a few centuries (war, climate collapse, misaligned AI), N might be close to zero. Drake described the equation less as a calculation and more as "an agenda for ignorance": a list of what we need to know.

  • Modern exoplanet data has tightened some variables. We now know that planets are extremely common. Most stars have them, and potentially habitable planets are abundant. This pushes some variables toward optimistic values. The biological and sociological variables remain entirely unknown.

  • The equation predicted exactly nothing, and that was the point. Drake never claimed it would give a final answer. Its value is that it forces you to think carefully about what kind of question you are asking, and which part of the answer you are most uncertain about.

The full story

Frank Drake and Green Bank

In November 1961, eleven scientists gathered at the National Radio Astronomy Observatory in Green Bank, West Virginia, for the first serious scientific conference on the search for intelligent extraterrestrial life. The participants included Carl Sagan and John Lilly. Drake, then 31, was hosting. He wanted to give the discussion some structure.

He wrote down his equation on a chalkboard. The conference participants spent the next few days estimating values for each term. Their final answer for N ranged between 1,000 and 100,000,000. The range was so large as to be almost useless, but it showed that the question was legitimate and worth pursuing.

The Fermi Paradox and the gap

Drake's equation says we should expect many civilisations. And yet we have detected no signal, no probe, no visitor. This contradiction is the Fermi Paradox, named for physicist Enrico Fermi who asked, over lunch, "where is everybody?" The Drake Equation and the Fermi Paradox are mirror images of the same question: the equation asks how many should exist; the paradox asks why we see none.

Why L matters so much

Of all the variables, L, the longevity of a communicating civilisation, is the one that most directly reflects our own situation. Drake estimated it as roughly the average lifetime of human civilisation so far. Since the Drake Equation was written, we have developed nuclear weapons capable of ending civilisation and have begun destabilising our own climate. Whether L for a typical civilisation is measured in centuries or millions of years may be the most important unknown in the equation.

Some researchers have proposed that the value of L is also the most useful information we could gather, not by contacting other civilisations, but by surviving long enough ourselves to become evidence that long-lived civilisations are possible.

Has the equation been solved?

No. And it may never be. The Drake Equation is a framework for thinking about a problem that spans biology, planetary science, astrophysics, and sociology. What it has done is make SETI, the Search for Extraterrestrial Intelligence, a scientifically respectable field, and provide a structure for updating our estimates as knowledge improves. The exoplanet revolution of the last thirty years has narrowed some uncertainties. The rest await either discovery or, more sobering, the accumulation of continued silence.

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