Drake equation calculator

What is the Drake equation?

N = R × fp × ne × fl × fi × fc × L. It breaks the question “how many civilizations in our galaxy could we detect right now?” into seven factors: R is the rate at which stars form per year, fp the fraction of stars with planets, ne the number of habitable planets per star that has planets, fl the fraction of those where life starts, fi the fraction of those that develop intelligence, fc the fraction of those that produce detectable signals, and L the number of years such a civilization stays detectable. Frank Drake wrote it in 1961 for the first SETI meeting at Green Bank, West Virginia.

What numbers did Drake use in 1961?

A 2012 paper in the International Journal of Astrobiology (Glade, Ballet and Bastien), citing Drake and Sobel, tabulates them as R = 10 stars per year, fp = 0.5, ne = 2, fl = 1, fi = 0.01, fc = 0.01 and L = 10,000 years, which gives N = 10. The 1961 estimates are often quoted in other forms too, so treat the preset as one published tabulation, not as the only version of what was said at the meeting.

Which of the seven factors do we actually know?

Only the first two or three have measurements behind them. Astronomers count star formation and, from planet surveys, the fraction of stars with planets and, roughly, with planets in the habitable zone. The last four factors, from the start of life to the lifetime of a civilization, have a single example on which to base an estimate: us. Sandberg, Drexler and Ord (2018) show that the honest ranges for those factors span many orders of magnitude.

What does the range mode do?

Instead of one number per factor you give a low and a high, and each factor is treated as equally likely at every power of ten between them (a log-uniform distribution, the choice used by Sandberg and colleagues). The median is exact and so is the mean. The chance that N is below one, and the 10th and 90th percentiles, come from 100,000 random draws with a fixed starting seed, so they are stable but approximate.

Why can the mean be far above the median?

When a factor is uncertain by many powers of ten, a few extreme draws dominate the average. With the Sandberg-style ranges on this page the median N is 0.032 while the mean is 2 × 10⁶. That is the point of the 2018 paper: a large average coexists with a large chance that the true value is tiny, so a large “expected number” does not make a crowded galaxy likely.

Does the Drake equation say aliens exist?

No. It is a way to organize ignorance, not a measurement. Put in optimistic values and you get millions, put in pessimistic ones and you get less than one. The three scenarios on this page are illustrations of that spread, not predictions. Nothing here is evidence for or against life elsewhere.

What does the Frank and Sullivan result add?

Adam Frank and W. T. Sullivan (2016) turned the question around: instead of estimating how many civilizations exist now, they asked how small the chance of a technological species per habitable-zone planet would have to be for ours to be the only one in the whole history of the observable universe. Their abstract gives about 10⁻²⁴; if the chance is higher than that, humanity was not the first or only technological species ever.

How to read the result

N is an expected number of civilizations that are sending detectable signals at this moment in the Milky Way. L matters most in practice: it is the time a civilization stays detectable, not the time it exists, and a civilization that goes quiet or never transmits does not count. Because the factors multiply, changing L by a factor of ten changes N by exactly the same factor. A value below 1 does not mean “zero civilizations”; it means the average over many galaxies like ours would be below one, so most would have none and a few would have some.

Worked example: from 10 to a thousand times fewer

With the 1961 values the product is 10: 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 10,000. Now keep everything else and let life start on only one habitable planet in a thousand (fl = 0.001). N falls to 0.01, far below one civilization, so on average a galaxy like ours would have none. Because the factors multiply, a single changed factor moves N by the same ratio. Using ranges, the Sandberg-style preset (their Table 1 ranges for R, fp, ne, fi, fc and L, and a wide fl range that is our own illustration, not theirs) gives a median N of 0.032, a mean of 2 × 10⁶ and about a 64% chance that N is below one. Change the fl range and the percentage changes with it.

What the 2018 paper showed

Sandberg, Drexler and Ord argue that the usual way of using the equation, plugging in single best guesses, hides the uncertainty and so creates the “Fermi paradox” (the puzzle of why we see no sign of others). Using ranges for each factor, they find an ex ante probability of 52 percent that we are alone in the Milky Way and 38 percent that we are alone in the observable universe, before any observation is taken into account. After accounting for the fact that we have not detected anyone, they report a range of 53 to 99.6 percent for being alone in the galaxy and 39 to 85 percent in the observable universe, depending on the kind of evidence considered. Their model of fl is more detailed than a single range, so the preset here is only in the spirit of the paper.

Limits of this method

The equation assumes the seven factors are independent, but they may not be: events such as nearby supernovae or the spread of life between planets could link them (Sandberg and colleagues test a few such correlations and find modest effects). It counts only civilizations that are detectable at the same time as us, so it says nothing about civilizations that came and went. It defines L as one number for all civilizations. And log-uniform ranges are a modeling choice that expresses ignorance, not knowledge: a different prior gives different percentages. For fun and for thinking, not for science funding decisions.

Sources: N. Glade, P. Ballet and O. Bastien, “A stochastic process approach of the Drake equation parameters,” International Journal of Astrobiology 11 (2012), Table 1, arXiv:1112.1506 (the 1961 values, after Drake and Sobel; not opened in the original); A. Sandberg, E. Drexler and T. Ord, “Dissolving the Fermi Paradox” (2018), Table 1 and conclusions, arXiv:1806.02404; A. Frank and W. T. Sullivan III, “A new empirical constraint on the prevalence of technological species in the universe” (2016), abstract, arXiv:1510.08837. The pessimistic and optimistic sets are illustrations by the site, not published estimates. Related: Schwarzschild radius calculator, redshift and Hubble’s law calculator, star magnitude calculator, orbital period calculator.