That is, if we include all and only the area within the Aurelian Walls.
For comparison, Manhattan is 33.77 square miles. Manhattan could hold 6.3 Romes.
If we include only the Republican city within the Servian Wall it’s even smaller, but I can’t seem to find a cite for the area. Nor for that within the Pomerium.
But New York City 130 years ago was just lower Manhattan. Much of upper Manhattan was near wilderness. “The Age of Innocence” has a scene showing this.
The Roman Forum is quite small and crammed with interesting stuff.
Hint we got from a guidebook which worked - buy your ticket at the Forum, not the Coliseum. The ticket is good for both, and the line is much, much, shorter. However the signs at the forum did not match the audio tour. This was shocking since we had just been in Berlin where museum audio tours and signs are perfect.
I was in Ephesus, in Turkey, a few years ago and was shocked at how ENORMOUS the city was. Now that was a damned big city, way bigger than the modern Turkish city of Selcuk, which is on that spot today.
During the Republican period it would have been that small, but during the 1st and 2nd century AD the lowest estimate is 450,000 and the average is one million. The census indicates over 40,000 apartment buildings called insulae in the city. The walls didn’t come close to enclosing the whole city.
Of course most of these people lived under conditions that were worse than the slums of Calcutta or Rio today.
Keep in mind that Rome had good public facilities. The average Roman had a hike to a public fountain or toilet or bath. Only the rich had running water and even they probably wouldn’t be connected to the sewage system. Most of the sewage ended up being dumped in the streets. A lot of the pipe they did have was made out of lead. Disease was always a constant problem and epidemics would periodically sweep through the city.
Even at that, it was better than what London or Paris had well up into the 19th century.