While there hasn't been an academic paper produced estimating, a number of quality surveys have been produced to let us answer the question of who many libertarians are there, and where are they. We've put together a quick summary of some of the best.
There are a lot more Libertarians than you thought.
At least between 10-20% of Americans are libertarians – similar to levels of liberals and conservatives – IntellectualTakeout.org
And whole lot of them live in Texas and the West. - Reason
Nearly a third of Millennials may be libertarian. – Reuters
1/3rd more likely than retirees - Pew
Hispanics 3x more likely to be libertarian than whites - Pew
Sources: Reuters, Reason, Fivethirtyeight.com, Cato Institute, Pew Research Center