Drake Equation Calculator: What It Does and Does Not Tell You
Drake Equation Calculator: seven numbers, three of them measured
N = R*·fp·ne·fl·fi·fc·L multiplies seven factors to get the number of civilisations we could hear from. Three of them have been measured. Four of them have never been measured at all, and the answer moves by a factor of ten every time one of those four does. This page does the arithmetic and shows you exactly where the answer comes from.
The seven factors, and what they multiply to
Work through the default numbers on this page: R* = 3 stars a year, f_p = 1, n_e = 0.37, the three biological fractions at 1, and L = 100 years. Then find out how much of that answer is evidence and how much is assumption.
Seven factors, multiplied
- N
- the number of civilisations in the Galaxy whose signals we could detect now. Not the number that have ever existed, and not the number that exist — only the ones broadcasting detectably at this moment.
- R*
- new stars formed per year. Measured. 1.65 ± 0.19 solar masses a year (Licquia & Newman 2015), which is a few stars a year depending on the average mass you assume.
- fp · ne
- the fraction of stars with planets, times the habitable-zone planets each has. Measured together. Kepler gives about 0.37 per star for Sun-like stars, with a 68% range of roughly 0.16 to 0.85. Splitting the product into two factors is historical; nothing measures them separately.
- fl
- fraction on which life appears. No measurement exists. One case, which we could not have failed to observe. Values from 10−30 to 1 are all consistent with the evidence.
- fi
- fraction of those where intelligence arises. No measurement exists. Same single case, four billion years later.
- fc
- fraction of those that broadcast detectably. No measurement exists, and the word “detectably” smuggles in the sensitivity of our own telescopes.
- L
- years a civilisation stays detectable. No measurement exists. N is directly proportional to it, so an assumption about L is an assumption about the answer. Ours is around a hundred years old and has not finished.
Worked example
Work through the default numbers on this page: R* = 3 stars a year, f_p = 1, n_e = 0.37, the three biological fractions at 1, and L = 100 years. Then find out how much of that answer is evidence and how much is assumption.
Do the measured part first, because it is the only part you can defend. R* × fp × ne = 3 × 1 × 0.37 = 1.11 habitable-zone planets formed in the Galaxy every year. That number rests on a published star formation rate and a published Kepler occurrence rate, and it is good to perhaps a factor of three.
Now the unmeasured part. fl × fi × fc = 1 × 1 × 1 = 1. We have set every one of these to its largest possible value, which says that life, intelligence and radio follow automatically wherever they can. There is no evidence for that, and none against it either.
Multiply by L. N = 1.11 × 1 × 100 = 111. Note what has happened dimensionally: the first three factors gave a rate, per year, and L turns it into a count. N is a rate multiplied by a lifetime, which is the only honest way to read the whole equation.
Now move one unmeasured box and watch. Set fl = 0.001, which is to say life gets going on one habitable planet in a thousand. N becomes 0.111. Nothing has changed about the Galaxy, no measurement has been contradicted, and the answer has fallen by a factor of a thousand to less than one.
Move L as well. Put L = 10 million years, which plenty of published estimates use. N climbs back to 11 100. So the same three measured factors support 0.111 and 11 100 equally well, a range of five orders of magnitude, and the spread comes entirely from factors no instrument has ever touched.
Finish with the number that actually matters. At N = 111 spread through the Galactic disc the nearest one is about 6000 light years away, so a question and its answer take about 12 000 years. Whatever N you end up believing, the distance row is the one that tells you what it would mean in practice.
Which factors are measured, and which are not
| Factor | What it means | What is actually known | Status |
|---|---|---|---|
| R* | new stars per year | 1.65 ± 0.19 solar masses per year (Licquia & Newman 2015); the count per year depends on the assumed average stellar mass | measured, to a factor of about two |
| fp · ne | habitable-zone planets per star | 0.37 (+0.48/−0.21) for Sun-like stars (Bryson et al. 2021) | measured, to a factor of about five |
| fl | fraction where life appears | one example, observed by the life it produced | no measurement |
| fi | fraction where intelligence appears | the same one example, about four billion years later | no measurement |
| fc | fraction that broadcast detectably | the same one example, for about a century so far | no measurement |
| L | years spent detectable | our own, currently around 100 years and unfinished | no measurement, and N is proportional to it |
The same three measured factors, five defensible sets of assumptions
| f_l | f_i | f_c | L (years) | N |
|---|---|---|---|---|
| 1 | 1 | 1 | 100 | 111 |
| 1 | 1 | 1 | 1 million | 1.11×106 |
| 0.1 | 0.01 | 0.5 | 10 000 | 5.55 |
| 0.001 | 0.001 | 0.001 | 1 billion | 1.11 |
| 10−6 | 10−6 | 1 | 1 million | 1.11×10−6 |
What the Drake equation is for, and what it cannot do
Frank Drake wrote this equation in 1961, before a small meeting at Green Bank, as a way of organising the discussion. It was an agenda: a list of the things you would have to know in order to answer the question, arranged so that the list multiplied out to the answer. It was never a prediction, and Drake said so repeatedly for the rest of his life. Understanding that is more useful than any number this page can produce.
The arithmetic is trivial and the inputs are the entire subject. Nothing about N is difficult except knowing what to put in, and for four of the seven boxes nobody knows — not approximately, not within a few orders of magnitude. A calculator that hands you N without saying so has told you a fact about its own defaults and dressed it up as a fact about the Galaxy.
What has genuinely changed since 1961. Two of the factors have moved from guesses to measurements, and that is a real achievement. The star formation rate is measured. The number of habitable-zone planets per star is measured, from thousands of transits, and it is large: planets are ordinary. In 1961 those two were the most uncertain things in the equation and the answer was dominated by them. They are now the solid part, and the whole uncertainty has moved into the biology and into L.
Why multiplying point estimates is the trap. If you put a single “reasonable” value in each box you get a single reasonable-looking answer, and it usually comes out in the hundreds or thousands — which makes the silence of the sky look like a paradox. Sandberg, Drexler and Ord (2018) redid the calculation with probability distributions in place of point estimates, using the actual spread of scientific opinion on each factor, and found a substantial probability that there is nobody else in the observable universe at all. The Fermi paradox, on that reading, is not a paradox but an artefact of the arithmetic we were using. You can see the same thing here by hand: the spread in N across equally defensible inputs is twelve orders of magnitude, and nothing in the point estimate shows you that.
Where this goes wrong in exam answers and in conversation. First, quoting someone else’s N as though it were a result. Second, mixing inconsistent factors: the star formation rate is for the whole Galaxy, while the occurrence rate is measured only for stars like the Sun, which are a minority — most stars are red dwarfs — so multiplying one by the other hides a correction nobody applies. This page does not apply it for you either, and that is worth knowing. Third, reading ne as a fraction when it is a number of planets and can exceed 1. Fourth, forgetting the units: the first three factors make a rate per year, and only L turns it into a count.
So what is the equation good for? Three things, all of them real. It tells you which measurements would change the answer, and that is why the exoplanet surveys matter. It makes the structure of the ignorance visible: you cannot hide a guess inside a product of seven factors once they are written down separately. And it gives you the distance, which is the part people skip — even an optimistic N puts the nearest neighbour thousands of light years away, so almost every answer to this equation implies that nobody is coming and nobody is holding a conversation. The light year and parsec page turns those distances into something you can picture.
Frequently asked questions
So how many civilisations are there?
Nobody knows, and this page will not tell you. What it will tell you is how much of any particular answer comes from measurement and how much from assumption. With the measured factors fixed, the published range of opinion on the other four spans about twelve orders of magnitude — from far less than one to many millions. Any source that gives you a single confident figure has quietly chosen four unmeasured numbers on your behalf.
Which parts of the equation are actually settled?
Two of them, and they are the two that used to be the worst. The Galaxy makes about 1.65 solar masses of new stars a year (Licquia and Newman 2015), which is a few stars a year. And rocky planets in the habitable zone are common: Bryson and colleagues (2021) get about 0.37 per Sun-like star, with a 68% range of roughly 0.16 to 0.85. Both numbers have real uncertainties, a factor of two to five, and both are honest measurements with published error bars. Nothing else in the equation is.
Why is N = L sometimes given as a shortcut?
Because if you choose the first six factors so that their product is about one civilisation appearing per year, then N is simply L in years. It was a popular way of putting it in the 1970s and it is a useful way to see which factor dominates — but it is an assumption dressed as a simplification. Our page gives you that product directly: look at the row that says how long a civilisation would have to last to give exactly one. If that row reads close to 1, then your N is close to your L.
Why does the answer jump about so much when I change one box?
Because N is proportional to every factor separately, so a factor of ten in any box is a factor of ten in N, and the uncertainties multiply rather than average out. Three factors that are each uncertain by a thousand give an N uncertain by a billion. The error propagation page does the general version: for a product, the relative uncertainties add in quadrature, which is tolerable at 10% and catastrophic at a factor of 1000.
Does a large N mean we should have heard something by now?
That is the Fermi question, and the distance row is why it is less sharp than it sounds. At N = 111 the nearest civilisation is around 6000 light years away, so its signal has to be strong enough to cross 6000 years of space and has to have been sent while there was anybody here to listen. We have also searched a very small fraction of the sky, over a narrow range of frequencies, for a few decades. The silence is real, but it is a weaker constraint than it feels.
Is the Drake equation science?
It is a correct piece of bookkeeping with inputs that are mostly unknown, which makes it a framework rather than a theory. It makes no prediction that could fail, because any N can be produced by choices nobody can rule out. That is not a criticism of Drake, who wrote it as a meeting agenda and was explicit about what it was. It is a criticism of the way it gets quoted — and the honest use of it is as a map of what we would need to measure next.
Related calculators
References
- T. C. Licquia and J. A. Newman, Improved Estimates of the Milky Way’s Stellar Mass and Star Formation Rate from Hierarchical Bayesian Meta-Analysis, The Astrophysical Journal 806, 96 (2015), arXiv:1407.1078. The abstract was read for this page: it gives a star formation rate of 1.65 ± 0.19 solar masses per year assuming a Kroupa initial mass function, and a total stellar mass of (6.08 ± 1.14)×1010 solar masses. The conversion from solar masses per year to stars per year is not in that paper and is done on this page by dividing by an average new-star mass of about half a solar mass.
- S. Bryson et al., The Occurrence of Rocky Habitable-zone Planets around Solar-like Stars from Kepler Data, The Astronomical Journal 161, 36 (2021), doi:10.3847/1538-3881/abc418, arXiv:2010.14812. The abstract was read for this page: η⊕ is given as 0.37 (+0.48/−0.21) to 0.60 (+0.90/−0.36) planets per star in the conservative habitable zone, and 0.58 to 0.88 in the optimistic one, for planets of 0.5–1.5 Earth radii around stars of 4800–6300 K, at 68% confidence. This page uses the lower, conservative figure.
- A. Sandberg, E. Drexler and T. Ord, Dissolving the Fermi Paradox, arXiv:1806.02404 (2018). The abstract was read for this page. It argues that Drake-style equations create the appearance of a paradox by treating highly uncertain parameters as though they were known, and that substituting realistic uncertainty distributions gives a substantial probability that there is no other intelligent life in the observable universe. No specific probability is quoted in the abstract, so none is quoted here.
- F. D. Drake, the equation as presented at the Green Bank conference on extraterrestrial intelligent life, November 1961. Cited for provenance: no contemporaneous document was read for this page, and the factors are given here in their standard modern form and order. Drake described the equation repeatedly as a way of organising the questions rather than as a means of answering them.
- International Astronomical Union, Resolution B3 on recommended nominal conversion constants for selected solar and planetary properties (XXIX General Assembly, 2015), together with the IAU definitions of the astronomical unit (exactly 149 597 870 700 m) and the parsec (648 000/π au). Resolution B3 fixes the nominal total solar irradiance at 1361 W m−2, the nominal solar luminosity at 3.828×1026 W and the nominal solar radius at 6.957×108 m. The resolution is explicit that these are agreed conversion factors chosen close to the best estimates, not measurements.