Is there an equation that can estimate chances of alien life in the universe? Seeing how infinite the universe appears and out of all of those stars, planets, galaxies, there must be other life forms. Mathematically, the odds are very good. Is there a mathematical equation to determine the chances of other life forms in the universe?
 A: Yep. It's called the Drake equation, named after Frank Drake. The equation is $$N=R_{\ast }\cdot f_{p}\cdot n_{e}\cdot f_{\ell }\cdot f_{i}\cdot f_{c}\cdot L$$ where $N$ is the number of civilizations in our galaxy with whom we could communicate (in other words, ones which are in our past light cone), $R_{\ast }$ is the average rate of star formation in our galaxy, $f_p$ is the fraction of those stars that have planets, $n_e$ is the average number of planets that can support life per star that has planets, $f_{\ell}$ is the fraction of planets that could support life that actually do support life at some point, $f_i$ is the fraction of planets with life that go on to develop civilizations, $f_c$ is the fraction of civilizations that have a technology that releases evidence of their existence into space, and $L$ is the length of time for which such civilizations release those detectable signals into space.
It's a probabilistic argument used to arrive at an estimate of the number of civilizations in the Milky Way. It was written as a way to stimulate dialogue at a SETI meeting.
The last four parameters are not known, and estimates range over several orders of magnitude which is kind of a lot. The usefulness in the equation, therefore, is not in the solving, but in the contemplation of all the various factors that must be considered when deciding the probability of extraterrestrial life. Some have proposed modifications to the equation, including factors such as colonization, the reappearance of intelligence after intelligence died out, and a Seager equation, which was proposed for the search for planets with biosignature gases. 
Specifically, some have used the equation to say we are probably alone in the Milky Way, and others have used it to say there are over 36 million other civilizations. There's also a bunch of criticism of the Drake equation.
Hope this helps!
A: Yeah, its called the Drake equation. Drake Equation  basically break down Milky Way into numbers to arrive at an estimate of how many communicating alien civilizations might be out there.
From Wikipedia 

This equation is a probabilistic argument used to arrive at an estimate of the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.
$$N=R_{\ast }\cdot f_{p}\cdot n_{e}\cdot f_{\ell }\cdot f_{i}\cdot f_{c}\cdot L$$ 
where $N =$ the number of civilizations in our galaxy with which communication might be possible (i.e. which are on our current past light cone),
   $R_{\ast }=$ is the average rate of star formation in our galaxy i.e. Milky Way,
   $f_p=$ the fraction of those with planets,
   $n_e=$ the average number of potentially habitable planets around those  stars,
   $f_{\ell}=$ the fraction of planets that could support life (that actually develop life at some point),
   $f_i=$ the fraction of those planets which develop intelligent life i.e. civilizations,
   $f_c=$ the fraction of civilizations that have a technology that releases evidence of their existence into space,
   $L=$  the length of time for which such civilizations release those detectable signals into space.

The equation was written in 1961 by Frank Drake, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at a meeting on the search for extraterrestrial intelligence (SETI). 

The last four parameters, $f_{\ell },f_{i},f_{c}$, and  $L$, are not known and are very hard to estimate, with values ranging over many orders of magnitude. Therefore, the usefulness of the Drake equation is not in the solving, but rather in the contemplation of all the various concepts which scientists must incorporate when considering the question of life elsewhere, and gives the question of life elsewhere a basis for scientific analysis.

Within the limits of our existing technology, any practical search for distant intelligent life must necessarily be a search for some manifestation of a distant technology. After about 50 years, the Drake equation is still of seminal importance because it is a 'road map' of what we need to learn in order to solve this fundamental existential question.
This video might clear up the topic better.
There another equation that uses planetary chemistry to calculate the odds  that life could form on a planet known as Scharf-Cronin equation. (more about it here)
$$N_{abiogenesis}(t) = N_b\cdot \frac{1}{n_0} \cdot f_c\cdot P_a\cdot  t$$
where  $N_{abiogenesis}(t)=$ the average number of origin of life 'events' that would occur on a planet during a certain length of time (t), 
$N_b=$ the number of potential building blocks (like atoms or molecules) for organism on a planet,
$\frac{1}{n_0}=$ the reciprocal of the average number of building blocks that can make a living system (e.g. a bacterium),
$ f_c=$ the fractional availability of those blocks (i.e. those not locked up in inaccessible states or conditions),
$P_a=$ the probability of an abiogenesis (origin) event per set of necessary building blocks per unit time, and finally the length of time in question,
$t=$ the length of time in question
This equation allows us to figure out how many planet can have any form of life (like micro-organisms, plants etc.). While in Drake equation it consider the life that is intelligent and able to sent signal out to space.
This video by DNews cover all the topic.
