The Drake Equation
Here is the equation:
N = R* x p x n x l x i x c x L
N is the number of civilizations in our galaxy who are technologically advanced enough that communication is possible. This number is a big lonely 1, plus the odd conspiracy theory and a caveat for our own relative ignorance as a youthful spacefaring civilization.
R* is the average rate of star formation per year in our galaxy. We have a reasonably good guess at this number, given large quantities of scientific data that have undergone much analysis over the years to arrive at it: NASA and the ESA come to 7 for our own galaxy.
p is the fraction of stars out of the sum total that have planets (exoplanets), while n is the average number of these planets that can support life per star. These quantities are a bit more up in the air, especially given recent developments in detecting exoplanets which have indicated that these numbers could in fact be quite high. The current estimate is generally between .2 to .6. Limiting the n value is our own bias that life must occur on Earth-like planets in an Earth-like way, known as the Rare Earth Hypothesis, making it almost infinitesimal. But what about silicon-based lifeforms as opposed to carbon, or even more exotic creations? The n value could very well be higher by fact of our limited imaginations.
l is the fraction of these planets that actually end up developing life; i is the fraction of those planets that develop intelligent life: those which develop civilizations; c is the fraction of those civilizations which develop technology that releases detectable signals into space; L is the length of time required for them to do so. These variables are, obviously, particularly resistant to attempts of quantification, or even just getting a ballpark guess. Our understanding of how civilizations develop as the general case is somewhat limited. Based on studies of our sole case—Earth—it has been proposed that the leap between favorable conditions towards life and the creation of life itself is not that big of one, though this is of course highly speculative and highly variable. The further leap from life to civilization took the better part of a billion years in our case, but can this number really be generalized to all potential civilizations? It's quite difficult to be scientific about these proposed quantities.
Keep in mind that the Drake Equation was never really intended to be an actual calculation, but rather, a general guide by which one can conduct thought experiments on the possibility of life on other planets. Many scientists, including Drake himself, have plugged numbers into this equation, but there is significant disagreement about them amongst the scientific community, including cries of arbitrariness and not enough evidence to make a legitimate attempt at calculating N.