Tens of thousands of people gathered today in Cairo's Tahrir Square. Or maybe it was a hundred thousand. Or could've been up to two million. Except, by some counts, the Square can't hold more than 225,000.

Every time a ton of people gather in one place, there are all sorts of pronouncements made about how many folks really showed. The figures rarely agree; Glenn Beck's rally on the National Mall this summer attracted a million people, according to Beck cohort Rep. Michelle Bachman. CBS News pegged it at more like 87,000.

There is something of a science, however, to sorting out crowd sizes. Here's how it works.

Step one: Get an eye in the sky. High-quality overhead imagery can give a pretty accurate sense of how many people are in a given spot below. For the 2009 inauguration, dueling estimators used everything from aerostats to satellites to snap shots of the masses.

Step two: Take a sample. Focus in on one small part of the crowd, and get a sense of its density. University of Illinois crowd-guru Clark McPhail figures a person can comfortably stand in five square feet. In tightly-packed situations, each person can squeeze into two-and-a-half square feet. Much more than that, and it's The Who at Cincinnati, 1979.

Step three: Measure the space. Get a sense of the square footage where the gathering is taking place. Tahrir Square is about 490,000 square feet, according to the private intelligence firm STRATFOR. At two-and-a-half-square feet per person – "comparable to the crowd density of a packed subway car" – even 200,000 activists would be pushing it. That figure sounds about right. Maybe there's a million people protesting in Cairo. But no way could they fit into that single spot.

This three-part method was first employed by a University of California at Berkeley journalism professor in the 1960s, who wanted to know how many anti-war protesters were outside his office. But despite advances in overhead imagery and statistical modeling, the seemingly-straightforward analytic exercise gets constantly mired in controversy.

The National Park Service, for example, used to be the go-to agency for official crowd estimates. Then it pronounced that only 400,000 people showed up to Louis Farrakhan's "Million Man March." Farrakhan threatened to sue. And the park service got out of the crowd-guessing game.

For President Obama's 2009 inaugural, the service relied on the Washington Post's figure of 1.8 million people. Competing estimates ranged from 800,000 to 1.271 million to "as many as two million."

Al Jazeera, the most influential news outlet covering the uprising, has revised its original protester count, from two million protesters in the protest epicenter to two million protesters in all of Cairo. But a strict count at a demonstration can be less influential than what networks broadcast. And with Al Jazeera keeping a densely packed Tahrir Square on people's TV screens, it gives the impression that all of Egypt is calling for Hosni Mubarak's head.

*Update 5:10 pm: *Dr. Clark McPhail, one of the godfathers of crowd-sizing science, e-mails in with his estimate:

I used Google Earth to access Tahrir Square in Cairo and the Google Earth Ruler to take some dimensions of the carrying capacity of the "square" as well as what appear to be accesible spaces surrounding it on three sides.

It is actually not square but a greenspace within a traffic circle. Assuming no traffic and that all lanes of the roadway that encompass Tahrir Square are included in the carrying capacity of that part of the venue, my calculations rounded off yield 84,000 square feet. At 5 sq. ft. per person this space could carry 16,876 people. When one looks at the photo, one could conceivable say the density is closer to 2.5 sq. ft. per person. The overhead vantage point of the photo is a useful one. That would yield 33,752 people.

My suspicion is that the gathering spreads out into the surrounding spaces that appear on the Google Earth map. There is a triangular space at the top of the Google Earth image of Tahrir Square as well as into the two polygons below the "square." The latter are not perfect rectangles but multisided polygons. I did not take precise measures but used to ruler to produce dimensions of the triangle above the "square" and of crude rectangles approximating those polygons below the "square." If anything this omits some accessible space. The "triangle" would accomodate 14,000 people at 5.0 sq ft, 28,000 at 2.5 sq. ft. The two "rectangles" would accomodate 21,000 at 5.0sq ft (42,000 at 2.5 sq. ft.) and 24,000 at 5.0 sq, ft, (48,000 at 2.5 sq. ft).

Combined the carrying capacity of those four spaces is roughly 380,457 sq. ft. This could accomodate 76,091 people at 5.0 sq ft per persons or 150,183 people at 2.5 sq. ft.

These are crude numbers but I would venture an estimate of 200,000 max for those four contiguous spaces. There are of course several streets that feed into the "square" and the possiblility of another 50,000 or so in those feeder spaces abutting the "square." I can't see how 1,000,000 people could fit into this venue.

Photo: AP/Tara Todras-Whitehill

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