When it comes to political demonstrations, claiming the advantage in crowd numbers is an old tradition. From Vietnam, to Glenn Beck's summer rally, it's common practice to claim millions marched, and Egypt's protests in Tahrir Square today are no different. Wired.com however, has a nice explanation of crowd sizing, that actually makes it pretty easy to sort out.
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.
So, yes, a lot of people are protesting against Hosni Mubarak. Maybe not a million. But a heck of a lot. And given he's rumored to be close to announcing that he won't run again, it's apparently enough.