Any question worth asking is worth asking with the condition "setting safety aside." So, setting safety aside, how many people could Times Square hold on New Year's Eve, if we really wanted to pack people in?

The city of New York estimates that some 2 million people will show up in Times Square to see the crystal-encrusted ball drop over the final 60 seconds of 2016. That's a lot of people, particularly given that the city is conscientious about maintaining clear lines of passage for emergencies and given that some part of the space is set aside for various news networks to host New Year's Eve programs of varying quality. (The hierarchy of gig quality for a pop band is sports arena in a big city -> sports arena in a small city -> big music festival -> small music festival -> NBC's New Year's Eve show -> NBC's pre-taped New Year's Eve show -> county fairs.)

But if we limit the discussion to the delineation above -- people watching the ball drop in Times Square -- there is basically no way that 2 million will crowd in to do so. The maximum, instead, is closer to 120,000, if we don't worry about any of those people needing to actually move.

Here's how the math works.

"Times Square" is somewhat loosely defined, but I suspect that most New Yorkers would define it as the area bounding Seventh Avenue and Broadway, between 42nd and 47th Streets. That's particularly the case for New Year's Eve, when we're really talking about that central open area in which everyone stands. Since the ball drops at the top of a building just south of 43rd Street, let's define the Times Square viewing area as the yellow part of this image.

Times Square, seen in Google Earth. (Google / The Washington Post)

Or, seen from above, as the grey on this map.

By drawing out that boundary, following the curves of the storefronts as best as we could, we are given an area that we can then translate into square feet, using this tool. But note the following:

  • This excludes any space for network broadcasts within the well of the square.
  • There are some obstructions that we're choosing to ignore here. That includes a set of risers at the north end of the square that overhangs a Broadway-ticket-sales booth and a military recruitment center. People can stand on the former; we're just going to ignore the latter.
  • This also excludes anyone on side streets and north of 49th as outside of Times Square and, importantly, excludes people watching from surrounding buildings.

The gray area on the map above yields an area of 17,221 square meters, or 185,360 square feet. That's the space into which we want to pack our crowd.

The question that ensues, then: How many people can we cram into a square meter?

There's a physical limit to how many people can fit into a space. On average, humans are about 18 inches wide at the shoulders and 10 inches deep, from the front of the chest to the back. That's an area of 1.25 square feet, meaning that we could fit 148,288 people into our Times Square area, packed in like a shipment of bookshelves to Ikea. Even by the standards of this exercise, that's not really realistic.

If you ask the hospitality industry, the ratio is about 10 people to every 100 square feet. Hilton hotels, for example, has a handy calculator letting you figure out how many people can fit within a space of a defined size for various types of event. For a reception, perhaps the closest analogue to our Times Square scenario, that results in a crowd size of 18,536 -- including, one assumes, high-topped tables and waiters passing around hors d'oeuvres.

For a more complete answer, we turn to the work of Dr. G. Keith Still, professor of Crowd Science at Manchester Metropolitan University in the United Kingdom. Still has offered expert testimony on the mechanics of crowds and crowd safety, including before Congress.

Still's in the business of setting aside the qualifier with which we began and, reached by email on Friday, indicated that the maximum number of people who could safely occupy a square meter of space in a crowd was five. Still's in the business of modeling crowds, and has created images showing what such a crowd would look like.

Five people per square meter in a 100-square-meter box. (Prof. G. Keith Still)

"When you exceed five, both the psychological and physical limits are reached," Still explained. "It begins to feel cramped and the risk of trips slips, falls and crowd surges increases exponentially above six or seven per square meter." He noted that demographics matter: Younger people take up less space.

He also noted that this was a stationary crowd. Once people start moving, things get tricky. He's filmed more-dense groups walking to show the difficulty of moving en masse. The visual below, excerpted from one of his videos, shows six men in one square meter walking down a street in Britain.

Six men walking in a one-meter loop of string. (Prof. G. Keith Still)

Remember our qualification, though: We don't care about safety. What's more, we're talking about a stationary crowd of fairly young people.

So let's jump from five to seven people per square meter, frustrating Still's attempts to preserve our physical health. That seems more realistic, according to his modeling, than, say, ten.

In that case, we're talking about seven people in each of 17,221 square meters of space -- a grand total of 120,547 people in Times Square.

Or about one-sixteenth of what New York City says the crowd will be.

People come and go on New Year's Eve, of course. People crowd into side streets; people pack restaurants around the square. People call friends who have offices overlooking the ball-drop and promise bottles of champagne in exchange for a spot near a window.

But the number of people watching the ball drop from within Times Square itself is nowhere near a million. Even if you assume that Ryan Seacrest and Anderson Cooper have to step down from their risers and literally rub elbows with the hoi polloi. And if you assume there are no hors d'oeuvres.