features a nice graph from a new paper comparing a sample of 128 African Americans to some Africans and to some European Americans
Each vertical bar represent one of the 128 African Americans. Blue represents the estimated European admixture, which averages 22%. All but one of the 128 African Americans appear to have some European ancestry, but about nine out of ten African Americans are at least half African by ancestry. In other words, when it comes to handing out affirmative action goodies, self-identification appears to be good enough for government work.
Most of the African ancestry is Yoruban, with only marginal amounts being pgyma (Mbuti) or Bushman (San).
Most of the small number of Europeans in the study cluster together (i.e., probably have no recent African ancestry), while two appear to have small amounts.
All this is pretty similar to what I heard from Penn State geneticist Mark Shriver eight years ago. He came up with about 18% white admixture in African Americans. The technology was more primitive then, but his sample size was about 20 times bigger. So, one-fifth appears to be a good rough estimate.