As the world watched protests in Egypt this week, everyone wanted to know just how many people were massing on the streets of Cairo. Yet crowd tallies reported by news media varied enormously.

Counting crowds, even in the age of satellite imagery and computerized scanning, remains a rough science. Getting an accurate measure depends heavily on the vagaries of weather and orbiting schedules—and on a mathematical shortcut devised by a former newspaper reporter 45 years ago.

The...