From Robert Louis Wilken, The First Thousand Years:
At the end of the first century there were fewer than ten thousand Christians in the Roman Empire. The population at the time numbered some sixty million, which meant that Christians made up one hundredth of one percent, or 0.0017 percent according to the figures of a contemporary sociologist. By the year 200, the number may have increased to a little more than two hundred thousand, still a tiny minority, under one percent (0.36). By the year 250, however, the number had risen to more than a million, almost two percent of the population. The most striking figure, however, comes two generations later. By the year 300 Christians made up 10 percent of the population, approximately six million.
All of these figures are estimates. Because there are no hard demographic data, they can be used only with other evidence. They show that in absolute numbers Christianity grew slowly at first, but the pace picked up in the third century, and if one were to draw a graph for the fourth century the line would mount in a steep upward curve. Christians could be found in all the major cities of the empire and in many smaller cities, and it was becoming apparent that Christianity was not a passing phenomenon. What is more, the Church attracted people from all walks of life and from all social classes, and its leaders were well educated, cultured, resourceful, and articulate.