Welcome to The Drake Equation

Calculations

Introduction

These pages guide you through a modified version of the Drake Equation. The formula provides a crude estimate of the number of technological civilizations in the Visible Universe. It does this by first multiplying together a series of numbers that estimate the quantity of habitable planets in the Universe and then multiplying this by a series of probabilities concerning the history of life on those planets.

We have included several simple exercises at the end to help you appreciate what your estimate implies about how close the nearest alien civilization may be, how common life itself may be, and how many technological civilizations have come and gone through the 13.8 billion years of cosmic history.

For more information about the original version of the Drake Equation and its history, use the "More About" button below. If you would like to read a personal statement by the person who designed this modified Drake Formula, use the "Statement" button below.

Astronomy buffs and professionals will notice that we make several crude approximations to keep the formula simple. We hope we will be forgiven for glossing over some complexities for the sake of obtaining a ballpark estimate.

We also apologize for software limitations on the way numbers are represented and displayed. We were unable to use sensible scientific notation throughout.

Use the Calculations button in the right corner above to start your Drake Equation Calculations.

Ng

Intro

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

Ng = The total number of galaxies in the Visible Universe.

The Universe is 13.8 billion years old, because the Big Bang occurred 13.8 billion years ago. It is not possible for us to receive light from any part of the Universe more than 13.8 billion light years away, because there has not been sufficient time for light to reach us from further away. This distance is called our "Cosmic Horizon." As a result, the part of the Universe observable by our telescopes, which we call the "Visible" Universe, is large but finite and contains a finite number of galaxies. Deep imaging with the Hubble Space Telescope suggests that the visible universe contains about 10¹² galaxies.

Enter for Ng the total number of galaxies in the Visible Universe in scientific notation, including both a number and a power of ten. To estimate the number of technical civilizations just in our galaxy, enter 1 x 10⁰.

Ng :

x 10

Then move to the next variable.

next Ng Ns fH nH fL fI fT L Nl next

Ns

Intro

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

Ns = The number of stars in a typical galaxy.

Our own Milky Way galaxy is fairly typical in terms of both diameter and number of stars. So enter here the approximate number of stars in the Milky Way. When you multiply Ng by Ns, you have an estimate for the total number of stars in the Visible Universe. A typical galaxy like our Milky Way contains about 10¹¹ stars.

Enter for Ns the number of stars in a typical galaxy in scientific notation, including both a number and a power of ten.

Ns :

x 10

Then move to the next variable.

next Ng Ns fH nH fL fI fT L Nl next

fH

Intro

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

fH = The fraction of stars that are able to support life.

Not all stars are likely to be suitable for supporting life. Some stars emit too much ultraviolet light; others do not last long enough. Some stars are binary or multiple stars in which planetary orbits at comfortable distances from the stars are not stable. Exotic types of stars, like neutron stars, are usually formed by violent processes that would destroy pre-existing planets. So, many stars are unlikely to be good hosts for planets or moons capable of sustaining life. However, if a planet's internal heat at the bottom of a deep ocean can support life, it is possible that the nature of the star does not matter too much. Considering all these factors and others you may know about, what fraction of the stars in the Visible Universe do you think are suitable hosts for "habitable" bodies, that is, planets or moons on which life could exist. (Note: fH should be between zero and one.)

Enter for fH the fraction of stars that are able to support life (a number between zero and one).

fH :

Then move to the next variable.

next Ng Ns fH nH fL fI fT L Nl next

nH

Intro

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

nH = The number of habitable planets or moons that actually exist around suitable stars.

By multiplying out Ng x Ns x fH , we estimated how many stars there are in the Visible Universe that might be suitable hosts for planets or moons that could support life. It is possible, however, that they do not have any suitable planets or moons or that they have more than one. Enter for nH , the average or typical number of habitable planets and moons that the suitable stars actually have. This number may be a decima fractionlike 0.001 or a whole number like 3 or 4, depending on what you think. Multiplying Ng x Ns x fH by nH then gives you an estimate for the number of planets and moons in the Visible Universe where life could survive. This does not mean that life is or was ever present there, just that it could be.

Enter for nH the number of habitable planets or moons that actually exist around suitable stars.

nH :

Then move to the next variable.

next Ng Ns fH nH fL fI fT L Nl next

fL

Intro

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

fL = The fraction of habitable planets or moons on which life actually does arise.

Conventional thinking on the origin of life supposes that this happens through a chemical evolution from pre-biotic materials to living organisms. However, it is also possible that life can be seeded from one body to another. When you multiply Ng x Ns x fH x nH by fL , then you are estimating the total number of planets or moons in the Visible Universe that have now or have ever had life on them by either process. (Note: fL should be between zero and one. Of course, life could evolve or be seeded more than once on the same body. All we care about here, though, is whether it arises at least once rather than not at all.)

Enter for fL the fraction of habitable planets or moons on which life actually does arise in scientific notation, including both a number and a power of ten. (The power of 10 must be zero or a negative number)

fL :

x 10

Then move to the next variable.

next Ng Ns fH nH fL fI fT L Nl next

fI

Intro

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

fI = The fraction of bodies with life on which intelligent life arises.

Ng x Ns x fH x nH x fL estimates the total number of planets and moons in the Visible Universe that have now or have ever had life of any sort. Of all of those, what fraction of them give rise to "intelligent" life forms? Please use some common sense in defining intelligence. For instance, most people would agree that porpoises and chimpanzees are fairly intelligent, while worms are not. Where you draw the line is controversial, so use your best judgment. Multiplying Ng x Ns x fH x nH x fL by fI now estimates how many planets or moons in the Visible Universe have now or ever have had intelligent life. (Note: fI should be between zero and one. Of course, intelligent life could evolve more than once on the same body. All we care about here, though, is whether it arises at least once rather than not at all.)

Enter for fI the fraction of bodies with life on which intelligent life arises in scientific notation, including both a number and a power of ten. (The power of 10 must be zero or a negative number)

fI :

x 10

Then move to the next variable.

next Ng Ns fH nH fL fI fT L Nl next

fT

Intro

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

fT = The fraction of worlds with intelligent life where one of the intelligent life forms develops a technological civilization.

Dogs are intelligent and can manipulate objects in creative ways at times, but they do not build cities or grow crops. Whales are probably more intelligent than dogs and may even have a culture of sorts, but they are also not technological. So, on what fraction of the worlds that develop intelligent life forms does at least one of them develop a technological civilization? By multiplying Ng x Ns x fH x nH x fL x fI by fT , you now have an estimate of the number of planets and moons in the Visible Universe that have now or ever have had technological civilizations. (Note: fT should be between zero and one. It may occur to you that technological civilizations could appear more than once on the same body. All we care about here, though, is whether it arises at least once rather than not at all.)

Enter for fT the fraction of worlds with intelligent life that develops a technological civilization in scientific notation, including both a number and a power of ten. (The power of 10 must be zero or a negative number)

fT :

x 10

Then move to the next variable.

next Ng Ns fH nH fL fI fT L Nl next

L

Intro

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

L = The total lifetime in years that technological civilizations typically last.

Technological civilizations, like everything else in the Universe, probably have a finite lifetime. Estimate how long you think the average technological civilizations might last. A thousand years? Ten thousand years? A million? A billion? Our Sun is about half way through its life cycle. If you think our technological civilization will survive as long as the Sun survives, then it will have a total life time roughly half the life of the Sun, or L = 5 x 10⁹ years).
It might help to decide what you mean by a technological civilization. If you define societies with cities and agriculture as technological, then humans have had a technological civilization for about 10,000 years. For instance, if you think our civilization is around 10,000 years old, but about to destroy itself, then L = 10,000 years. This is crude, but we are after an estimate here, not a precise number.

Enter for L your estimate for the lifetime of a technological civilization in years, including both a number and a power of ten.

L :

x 10

You can go back to any variable or on to the final calculation.

next Ng Ns fH nH fL fI fT L Nl next

NI

Intro Explore Further

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

How many technical civilizations now in the visible universe?

NI :

How many technical civilizations per galaxy now?

Now:

What is the average distance to the nearest civilization in light years?

Light Years :

How many technical civilizations have ever existed in the current volume of the visible universe? Learn more

The number of active technological civilizations in the Visible Universe depends on how long you think they last, on average. Most likely, alien civilizations come and go. We could ask, in all of cosmic history up until now, about how many technological civilizations have ever existed in the volume of our current Visible Universe? We obtain that number by NOT considering the finite lifetime of intelligent civilizations.
The approximate number of technological civilizations that have appeared throughout the current volume of the Visible Universe in all the 13.7 billion years of cosmic history.

Ever:

You can go back to any variable and change your entry.

next Ng Ns fH nH fL fI fT L Nl next

Personal Statement

Intro

Personal Statement by Richard H. Durisen

Some of the most profound questions that human beings can ask about the Universe concern our place in the grand scheme. How did the world around us and we ourselves come to be? How common in the Universe are sentient beings like ourselves who live in complex technological societies and who ask similar questions about the Universe around them? Although the existence of extraterrestrial life has few practical consequences for our day-to-day lives, people can and do have strong feelings and opinions about it. In many ways, speculation about intelligent extraterrestrials has taken the place in our psyche formerly occupied by myths about the "gods" in earlier human cultures.

The scientific study of possible life in the Universe beyond the Earth, including intelligent life, is the young and growing field of inquiry called "astrobiology" http://www.astrobio.net/. Roughly speaking, "scientific" means using arguments from concrete, verifiable evidence, where the arguments are constrained to be consistent with what we already know about how the Universe works. Although questions about life in the Universe can be posed scientifically, there are currently no universally accepted answers. Using the same common body of relevant information and scientific principles, some scientists can and do argue that intelligent life is common in the Universe, while others argue that it is rare. Unfortunately, there are no higher authorities to which a scientist can appeal for definitive answers. Science is, by its nature, an entirely human activity based on strict rules of evidence. As we continue to explore the Solar System, we anticipate, in the foreseeable future, having more concrete evidence, one way or the other, about the prevalence of simple, primitive life forms. There is also the remote possibility that SETI (Search for ExtraTerrestrial Intelligence http://www.seti-inst.edu/) scientists may succeed during our lifetimes in detecting radio signals of intelligent origin from beyond our own planetary system. Meanwhile, we can make rational arguments and speculations based on current knowledge.

Our Web pages, built around a modified version of the Drake Formula, attempt to guide your thinking by analyzing the question, "How many technological civilizations are there in the Visible Universe?" The analysis proceeds by breaking this big question into a series of sub-questions. As you will see, some of these sub-questions can now be answered with some certainty while others cannot be answered at all at the present time. We hope that these Web pages will help you develop a more informed opinion about life in the Universe by guiding you through this thought process.

I would like to add, by way of acknowledgment, that the design and implementation of these Web pages with my collaborators Glenn, Julia, and David was a joyful and stimulating journey of discovery, full of surprises and "Aha" experiences. I hope you will have as much fun playing with them as we had during their creation.

Thanks also to Frank Morris, who adapted the original Drake Formula calculator for use on mobile devices.

More About the Drake Equation

Intro

Learn More about the Search for Extraterrestrial Life

The following external sources offer further information about the search for extraterrestrial life and the Drake Formula.

Check out the Astrobiology Magazine

The SETI Institute in California provides information about the search for intelligent life in the Universe. The SETI Institute also offers its own version of the Drake Equation calculator.

Wikipedia offers excellent discussions about the Drake Equation and about astronomer Frank Drake, who originally developed the Drake Equation.

Enjoy!

Explore Further

Calcutations

Ng x Ns x fH x nH x fL x fI x fT x L = Nl

How many technical civilizations have ever existed in the Milky Way? Learn more

In our Milky Way galaxy alone, the number of technological civilizations that have appeared so far.

NI:

How many habitable bodies exist in the visible universe? Learn more

The number of habitable planets and moons in the Visible Universe depends only on multiplying together Ng, Ns, fH, and nH.

Habitable Bodies:

How many habitable bodies developed simple life in the visible universe? Learn more

Of these habitable bodies, the number of worlds that have had at least a simple form of life depends on multiplying together Ng, Ns, fH, nH, and fL.

With Simple Life:

How many habitable bodies exist in the Milky Way? Learn more

Numbers within our own Milky Way may be easier to grasp. We get estimates for these through not multiplying by Ng. The numbers of habitable planets and moons in the Milky Way depends only on multiplying together Ns, fH, and nH.

In Our Galaxy:

How many habitable bodies have simple life in the Milky Way? Learn more

The number of worlds in the Milky Way that have had at least a simple form of life depends on multiplying together Ns, fH, nH and fL.

With Simple Life:

How many habitable bodies in the visible universe ever developed intelligent life? Learn more

The number of habitable planets and moons in the Visible Universe on which life progressed from simple to "intelligent" forms (cows, wallabies, dogs, dolphins, apes...you decide) depends on multiplying together only Ng, Ns, fH, nH, fL, and fI.

With Intelligent Life:

How many habitable bodies in the Milky Way ever developed intelligent life? Learn more

If you find numbers within our own Milky Way galaxy easier to grasp, then do not multiply by NG. The numbers of planets or moons in the Milky Way that have ever had intelligent life depends only on multiplying together Ns, fH, nH, fL, and fI.

With Intelligent Life: