(according to the latest estimations and the defaults filled in above)
Frank Drake wrote this equation in 1961 for a meeting at Green Bank. It was never meant to produce an answer. It was an agenda: seven things you would need to know, in the order you would need to know them.
In the sixty-five years since, astronomy has answered the first three. The last four have not moved at all. The defaults above reflect that split exactly: modern measurements in the first three fields, and Drake's own 1961 numbers still sitting in the other four, because nothing better exists.
How many stars are born (R*). The Milky Way forms about 1.9 ± 0.4 solar masses of new stars per year, from a survey of the whole galactic plane (Chomiuk & Povich 2011, confirmed at 2.0 ± 0.7 by Herschel, Elia et al. 2022). There is a catch worth knowing: the equation wants a number of stars, and what gets measured is a mass. Converting between the two depends on how that mass is split, and published conversions run from one to three stars a year up to six or seven, because most new stars are small red dwarfs. Drake used 1.
How many have planets (fp). Microlensing surveys found that planets are the rule rather than the exception, with at least one bound planet per star (Cassan et al., Nature 2012). Counted directly rather than extrapolated, Kepler sees planets around about 30% of Sun-like stars, and the authors of that measurement note it does not directly answer this question (Zhu & Dong 2021). So 100% is defensible, but it is an inference, not a headcount.
How many sit in the habitable zone (ne). About 0.37 planets per star, Earth-sized and in the conservative habitable zone of a Sun-like star, with a 68% interval running from 0.16 to 0.85 (Bryson et al. 2021). Loosen the definition of the zone and it rises to 0.88. Kepler could not see far enough out to catch Sun-like habitable zones directly, so every value here is a model-dependent extrapolation, and a 2025 review exists specifically because the field has no consensus on it (Fernandes et al. 2025).
The habitable zone is a temperature band. It says nothing about whether a planet has held on to an atmosphere. TRAPPIST-1 is the first system where that has been tested, and the results arrived in 2025 and 2026:
| Planet | What JWST found |
|---|---|
| TRAPPIST-1 b | Dayside 490 K, no detectable nightside emission. Consistent with a bare rock. Atmospheres above 1 bar strongly disfavoured. Gillon et al. |
| TRAPPIST-1 c | Same treatment, same conclusion. |
| TRAPPIST-1 d | Flat spectrum. Titan-like, Venus-like, early Mars and modern Earth analogues all rejected above 95%. Piaulet-Ghorayeb et al. 2025 |
| TRAPPIST-1 e | The one actually in the habitable zone. Four transits, and the answer is still open: a nitrogen-rich atmosphere fits, and so does no atmosphere at all. Glidden et al. 2025 |
Three of the three planets that have been tested look airless. The fourth is undetermined. That is one system, around one red dwarf, so it settles nothing about the galaxy. It does mean that ne counts a temperature range and not a place where anything could live.
From fl onward there is no data at all. Not thin data, not contested data: none. Every number ever published for these four is a prior, an assumption or a convention, and the sample size is one planet.
Does life start (fl). Life appeared on Earth quickly, which looks like evidence that it is easy. Run that argument properly and it depends almost entirely on the prior you start with, and it stays consistent with an arbitrarily small probability (Spiegel & Turner 2012). A more careful treatment that corrects for the fact that we could only exist on a planet where life started early puts the odds at 13 to 1 that abiogenesis is fast on an Earth analogue (Kipping 2025). That is a bet, not a count. Finding a second, independent origin of life anywhere would change this parameter more than any other single discovery.
Does intelligence follow (fi). Two positions, one fossil record. The hard-steps model says human origins required passing several intrinsically improbable filters, so technological life is close to unique. A 2025 reassessment argues the opposite: that the delays were planetary rather than improbable, that Earth had to become habitable for us in stages, and that humans may be the expected outcome of that process (Mills, Macalady, Frank & Wright, Science Advances 2025).
Do they broadcast (fc). Drake meant radio. The field now says technosignatures, which also covers laser pulses, industrial pollution in an atmosphere, waste heat and megastructures (NASA Technosignatures Workshop 2018). Widening the definition raises this number without anyone having measured anything.
How long do they last (L). This is the one that decides the answer. It is the only parameter with units of time, so N scales with it directly, and the honest range covers six orders of magnitude. Drake guessed 10,000 years. The Green Bank meeting settled on somewhere between 1,000 and 100,000,000. Westby & Conselice (2020) used 100, on the reasoning that a century is all we have managed so far. Set L to 100 and the galaxy is nearly empty; set it to a million and it is crowded. Nothing in physics or biology tells you which.
Sixty years of listening is itself a measurement, and it is the only empirical constraint on the answer as a whole. Breakthrough Listen puts an upper limit of 0.066% on the fraction of stellar systems within 50 parsecs carrying a strong transmitter (Wlodarczyk-Sroka, Garrett & Siemion 2020). Turning the whole non-detection into a rate gives fewer than one to five signal emissions per century across the galaxy at 95% credibility, with an expected wait of 60 to 1,800 years before the next one (Grimaldi 2023).
If your answer above runs into the thousands, that is the number it has to sit next to.
| N | Who, and on what assumption |
|---|---|
| 1,000 to 100,000,000 | The Green Bank meeting, 1961 |
| ~1,000,000 | Sagan, averaging an optimistic and a pessimistic lifetime |
| 36 (+175 / −32) | Westby & Conselice 2020, assuming L = 100 years. The nearest would be 17,000 light years away, far beyond detection. |
| median 0.32 | Sandberg, Drexler & Ord 2018, replacing point estimates with honest probability distributions |
That last one is usually reported as "scientists say we are alone", and that is not what it says. Their point is about method. Feed the equation seven single numbers and you get false precision. Feed it the actual spread of scientific opinion on each term and the result spans thirty orders of magnitude, wide enough that "nobody else" sits comfortably inside it. Their conclusion is that the silence needs no exotic explanation, because on what we honestly know, silence was always a likely outcome.
Which is the thing to take away from the box above. The number it gives you is real arithmetic on real inputs. Three of those inputs are measurements with error bars. Four are a guess someone made at a meeting in 1961, and multiplying a measurement by a guess gives you a guess.
Set the fields above to anything mildly optimistic and you get a galaxy with company in it. That is where Enrico Fermi's question from 1950 bites. If they are out there, and have been for billions of years, where are they?
The force of the question comes from arithmetic about time, not distance. A civilisation that sends out self-replicating probes at a tenth of light speed, each one building copies at the next system, would reach every star in the galaxy within a few million years. The galaxy is around thirteen billion years old. Any civilisation that ever wanted to spread and got started even slightly early has had a thousand chances over to finish the job. One would have been enough.
And there is nothing. Sixty-five years of listening, a hundred million dollars of Breakthrough Listen, no confirmed signal. Not one.
This is where the last field above does more work than it looks like it does. L is usually read as "how long a civilisation lasts". What it actually sets is how much of the galaxy's history any two civilisations share.
Picture the galaxy as a dark room and each civilisation as a struck match. With L at a century, every match burns for a hundred years against thirteen billion. Millions of them could have flared already and every single one would have gone out before the next was lit. A galaxy that has held a million civilisations, and never two at the same time, looks exactly like an empty one from the inside.
It gets worse for the observer, because ruins do not wait either. Stone monuments erode over thousands of years and almost nothing built survives recognisably past a hundred thousand. Across interstellar distance, a civilisation that ended a million years ago leaves us nothing to find. Silence is what a graveyard sounds like too.
Robin Hanson's framing from 1998 is the cleanest way to hold this. Somewhere on the road from lifeless rock to galaxy-spanning civilisation there is at least one step that almost nothing gets past (The Great Filter). The equation above is that road, written out. The only question is which of the seven steps holds the filter.
If it is behind us, one of the early terms is far smaller than the defaults suggest. Perhaps life almost never starts. Perhaps it starts often but stays single-celled: on Earth, the merger that produced complex cells appears to have happened once in four billion years. Perhaps intelligence is the fluke, arising once among hundreds of millions of species. In that case we are through the hard part, and the silence around us is simply how rare we are.
If it is ahead of us, the early terms are as generous as they look, the galaxy has produced civilisations repeatedly, and something reliably stops them at roughly the stage we have just reached. We went from agriculture to nuclear weapons in ten thousand years and from nuclear weapons to now in eighty. On several documented occasions during the Cold War, whether the exchange started came down to one officer's judgement. A two percent chance of ending yourself per century is a rounding error over one lifetime and a certainty over a hundred thousand years.
The filter also need not be one wall. Fifty consecutive steps, each survived nine times out of ten, leaves roughly half a percent standing. No single step looks impossible and almost nobody arrives.
Nick Bostrom drew the conclusion most people find backwards (Where Are They?, 2008). We know roughly how empty the sky is. That emptiness has to be explained by a filter somewhere. Every discovery that makes the early steps look easy, microbes under the Martian surface, an independent origin in Europa's ocean, moves the filter later, and later means closer to us.
A galaxy where life turns out to be common and the sky is still silent is a galaxy that is killing something. The most comfortable finding remains the one we keep getting: nothing out there at all.
Which turns the box at the top of this page into something other than a curiosity. Seven numbers, three of them measured, four of them still a guess from 1961. Pick your guesses and you are not really estimating how many neighbours we have. You are picking which of those seven steps you think almost nothing survives, and whether you think we have already been through it.