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How many Romans would use an average-sized balneum every day, if the people coming to the balneum only went to that balneum once a day?

I have already tried researching about this question using different wording, but each time I just get insufficient or irrelevant links, so that is why I used SE.

I apologise in advance if my question is incorrectly worded...

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    Welcome to History:SE. What has your research shown you so far? Where have you already searched? What did you find? Please help us to help you. You might find it helpful to review our Help Centre and, in particular, How to Ask. – sempaiscuba Sep 24 at 19:52
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Depends on the size of the balneum, the size of the community, and the number of competitors.

"Small bathhouses, called balneum (plural balnea), might be privately owned, while they were public in the sense that they were open to the populace for a fee. " Wikipedia

"These Roman baths varied from simple to exceedingly elaborate structures, and they varied in size, arrangement, and decoration. " ibid

"Such was the importance of baths to Romans that a catalogue of buildings in Rome from 354 AD documented 952 baths of varying sizes in the city." ibid

According to Rome: A Living Portrait of an Ancient City, pp230 Augustus counted more than 170 in Rome in 33 BCE; four centuries later the number was nearer a thousand. That source also contains some information about balnea/region - if you were interested, you could outline a rough statistical model.

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It would be very difficult to define a meaningful general average, especially without more clearly defined parameters. As @Mark-C-Wallace has explained, the sizes of individual balneum varied widely. Their popularity and availability would have depended on where (the city of Rome itself, or the wider empire) and when (Roman bath culture spanned centuries) you are referring to.

Here are some helpful numbers to give some perspective though:

How popular the bathhouses were we could conclude from the fact that in 33 BC, there were 170 of them (public and private) in Rome alone. By the end of the 4th century AD, there were 11 public (some of them with a capacity of 2, 000 - 3, 000 bathers per day!) and 926 private baths in the Eternal City.

The largest complex of all was the Baths of Diocletian. According to this page, 3,000 was the upper range of it's daily visitor load. But this seems to be a conservative estimate and may have actually been what it accommodated at one time. The second largest complex was the Baths of Caracalla, and according to Wikipedia it could accomodate 6,000 to 8,000 bathers daily.

Based on these few data points, we might say that if we were only counting the major public balneum and ignoring the far more numerous privately-owned ones, daily average visitors peaked at least in the hundreds if not the thousands. A more inclusive average would have to be far lower.

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