They used a theory called the Astrobiological Copernican Limit, which is when scientists apply evolution on a cosmic scale.
Their calculation is a refinement of one first thought up in 1961 by Francis Drake, who set seven criteria for alien life, ranging from the number of stars in the galaxy to the presence of detectable electronic signals.
However, estimates using this equation are far-ranging, from zero to many billions.
There are two Astrobiological Copernican Limits, which dictate that intelligent life forms in less than five billion years, or after about five billion years, based on the fact that on Earth a communicating civilisation formed after 4.5 billion years.
Intelligent life would only form in this time for planets which are, like Earth, within a star's habitable zone and have the right distribution of elements.
First author of the paper Tom Westby said: "In the strong criteria, whereby a metal content equal to that of the Sun is needed (the Sun is relatively speaking quite metal rich), we calculate that there should be around 36 active civilisations in our galaxy."
Scientists estimated the number of Communicating Extra-Terrestrial Intelligent civilisations, which are civilisations similar to those on Earth, which broadcast radio signals into space, by using these limits.
Christopher Conselice, professor of Astrophysics at the University of Nottingham, who led the research, said: "There should be at least a few dozen active civilisations in our Galaxy under the assumption that it takes five billion years for intelligent life to form on other planets, as on Earth."
Another factor in the equation is how long the technology used by intelligent civilisations, such as televisions and satellites, broadcasts signals into space.
Our technological civilisation is 100 years old, and if others are of a similar age then there will be about 36 ongoing intelligent technical civilisations throughout our galaxy.
If all the civilisations were found, the scientists said, they could work out how long humanity is likely to survive.