The numbers on the growth of Christianity in the Roman Empire are very uncertain, but there are enough data points to hazard a reasonable estimate.
It is generally agreed that Christians, having started with a few dozen adherents in 30 AD, made up ten percent of the Empire by c. 300 AD, that is six million people, and that by c. 350 that figure was over thirty million, with Christians now a clear majority of the Empire.
Rodney Stark in The Rise of Christianity has a very interesting model that starts with 1,000 members of the Jesus Sect in 40 AD and projects a growth rate of 40% per decade up to the fourth century. As Stark lays out, this tallies with the available historical evidence, both the more impressionistic kind, and a remarkable study on the growth of Christianity in Egypt, where we have the nearest approximation to BMD records in the Roman world.
Starks model means the trajectory was, roughly:
- 7,500 Christians by the end of the first century (0.02% of sixty million people);
- 40,000 Christians by 150 AD (0.07%)
- 200,000 by 200 AD (0.35%)
- 2 million by 250 AD (2%)
Again, Stark’s numbers tally with what had long been known from a triangulation of the sources: there is a widespread sense of a massive explosion in Christian numbers in the second half of the third century—and there was, in absolute terms. The numbers do not seem to have, and do not need to have, changed in a relative sense at all. Stark underlines this point because it cuts against one of the standard arguments in the historiography, namely that miracles—either literal or illusory (depending on the historian)—are a necessary explainer of what happened, whereas “resorting to simple arithmetic” will do it.
The growth model Stark presents, he freely concedes, smooths over some of the “bumps”.
There were undoubtedly periods of faster growth, and there were some very serious setbacks in the rounds of persecution, especially in the 60s AD when, exaggerated though some accounts might be about how many Christians the Emperor Nero (r. 54–68) killed after the great fire of Rome, even a few hundred deaths would be a severe blow to a community that consisted of at most 2,500 people. The Jerusalem community of Christians was, if not entirely destroyed, lastingly downgraded and diminished in this period by the persecution and its own political decisions during the Jewish revolt (66–73).
As well as variations in time, presenting numbers for the whole Empire obscures the geography of early Christianity, which was very heavily concentrated in the Eastern half up through the third century, in Anatolia, Egypt, and North Africa, and Christians were concentrated in the cities, hence the word paganus (“pagan”) for their opponents, a word meaning “countryman” or perhaps more precisely “countryside man”.
Acknowledging these caveats, it should nonetheless be obvious that providing a vision of the big picture—at the expense of some detail—is what averages are for.
A key implication, drawn out by Stark, is that Constantine (r. 306–37) was following the Roman people rather than leading them in adopting Christianity in 312, and that whatever help it gave to the Christian cause for the restrictions and persecution to be dropped, and the social desirability of Christian belief to be raised, Constantine did little more than bring forward the date of something that was in train anyway and that he could not have stopped.
That said, contrary to some cynical historiography, at the time Constantine adopted Christianity the numbers were still too small to be any use in a bid for power. Indeed, even if the numbers are under-estimated, Christians were simply in no position to assist: an aspiring Emperor needed the senatorial class, the equites, and above all the legions; this aristocratic elite and the army were not only all pagan, but committedly so, making Christianity, if anything, a disadvantage. Christianity, up to the beginning of the fourth century and for some time after overwhelmingly consisted of slaves, the peregrini (pre-212 “foreigners”, non-citizens), and lower-class urbanites; this coalition, the subject of relentless mockery in pagan polemic, counted for nothing in Rome. It was only after Christianity had prevailed, and its moral assumptions had replaced those of the Classical world, that a concern for the views of the lowest became a norm, that weakness became a kind of strength.
Looking at how Christianity spread, logistically, Bart Ehrman in The Triumph of Christianity underlines two factors. First, Christianity, because of its doctrine, was a missionary faith—something entirely new to the ancient world—and Paul’s theological innovation, making it possible to be Christian without being Jewish, lifting the requirement for circumcision and the dietary laws, meant the Jesus Sect was no longer restricted to trying to convert the most resistant community (Jews) and instead had access to a universal recruitment pool of gentiles. “Pagan” religions did not proselytise because—and this is the second factor—pagans did not regard “religions” as exclusive. For pagans, defining themselves by which god they primarily worshipped would have seemed as strange as defining themselves by their favourite food, Ehrman argues. More seriously, in the pagan mental universe, “There was no sense that a person who turned to a new cult had to turn away from another”; to add a new god did not mean rejecting the old. By upending these assumptions, Christians proceeded in a manner that not only advanced their own cause but simultaneously killed off paganism; every convert to Christianity was a subtraction from paganism.
What is most fascinating, relating very much to the issue of Constantine’s conversion and its role in Christian/Western history, is that while Christianity was a missionary faith in doctrine and outlook, it did not really have any missionaries after Jesus’ brother James and Saint Paul were executed in the 60s AD, and evangelists of the Pauline kind only really return to the scene after Christianity triumphs under Emperor Theodosius (r. 379–95).
How, then, if not by organised missionary work with battalions of door-knockers, mass open-air rallies to convert multitudes, and the rest of it, did Christianity get so far in just three centuries? In the simplest way of all: through social interactions. Word of mouth between neighbours, co-workers, traders, even slaves, who were being transported all around the Empire, transmitted this new faith, and because of the structural fact of what it meant to be a convert, the exclusivity of it, Christianity ate its way through the pagan world, the winner of a race the others didn’t even realise was underway.
Post has been updated
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 Rodney Stark, 1996, The Rise of Christianity, pp. 7-10.
 Roger S. Bagnali, 1982, Religious Conversion and Onomastic Change in Early Byzantine Egypt. The book utilises the Oxyrhynchus Papyri.
 Stark, The Rise of Christianity, p. 7.
 Stark, The Rise of Christianity, p. 12.
 W.H.C. Frend, 1965, Martyrdom and Persecution in the Early Church, pp. 170-71.
 For a discussion of these dynamics see: Bart Ehrman, 2018, The Triumph of Christianity, chapter eight.
 An example of this kind of mocking polemic is The True Word, written in the 240s, which we know about from the quotations in the refutation, Contra Celsum (Against Celsus), written by one of the most important church fathers, Origen (d. c. 254).
 Ehrman, The Triumph of Christianity, pp. 120-21.
 The identifiable exceptions between Nero’s time and the Theodosian era, such as Gregory of Neocaesarea (d. c. 270), the “wonder-worker” who is supposed to have only had seventeen Christians in his diocese when he became Bishop of Pontus and when he died there were only seventeen pagans, were exceptions that prove the rule: these are local figures working in their hometowns. This would apply to Pantaenus (d. c. 200), himself a proselyte, in Alexandria; Saint Denis of Paris (d. c. 250), if he ever lived; Martin of Tours (d. 397); and Porphyry of Gaza (d. 420). See: Ehrman, The Triumph of Christianity, p. 118.
Figures like Frumentius (d. 383) in Ethiopia and Wulfila/Ulfilas (d. 383), who is supposed to have taken a translation of the Bible to convert his fellow Goths, were working outside the Empire so did not affect the growth of Christianity within, and the information about such foreign missions is sporadic and murky. By the time of Saint Patrick (d. 461) going to in Ireland, Christianity has already triumphed.
The medieval period is clearer, beginning with the Roman Church’s mission to Britain in 597 that leads on to Boniface (d. 754) et al. converting northern Europe, and Alopen in China from 635.
 The activities of the Cappadocian Fathers in the fourth century, running essentially a welfare state throughout the Empire, is more typical of how Christianity spread: by contact and example, not proselytism in a strict sense. While the common tropes of evangelism and miracles turn out not to be so significant, charity work and the theology behind it that gave an equal worth to every human irrespective of social station were key factors in attracting people who encountered Christianity to adopt it.
The fact that caring for the needy was a key aspect in Christianity out-competing paganism was attested to by no less a figure than the Emperor, Julian “the Apostate”, the only post-Constantine ruler to try to roll back Christianity. In 362, Julian wrote to the priests of Cybele, to complain that it was “shameful” they had not been providing for the poor, when the Christians “support not only their own poor, but ours as well”. Julian wanted Cybele’s galli to demonstrate that “good works was our practice of old”. For a cult whose central practice for maybe 1,000 years was self-castration at an annual ceremony that consisted of cross-dressing and dancing, this was something of a shock. See: Tom Holland, 2019, Dominion: The Making of the Western Mind, p. 145-7.
 This argument is laid out in Ramsay MacMullen, 1984, Christianizing the Roman Empire: AD 100 – 400. See also The Triumph of Christianity, pp. 117-19.