Since at least the 19th century, people have periodically claimed to see giant snowflakes falling from the sky — big ones the size of saucers and plates or even larger, their edges turned up, their heaviness making them descend faster than small flakes.

But the evidence was always sketchy and, because of the fragile nature of snowflakes, fleeting. The giant flakes were not quite in the category of sea monsters or U.F.O.’s. Even so, skeptics noted the human fondness for exaggeration, as well as the lack of convincing photographs. And the organizations that compile weather records never made tracking big flakes an observational requirement. So the giants languished in a twilight world of science, their existence claimed but seldom documented.

Now, theorists, weather historians and field observers are concluding that most of the reports are true and that unusually large snowflakes two to six inches wide and perhaps wider fall regularly around the globe, surprisingly big and fluffy, if seldom witnessed or celebrated. Guinness World Records lists the largest snowflakes as having fallen during a storm in January 1887 at Fort Keogh, in Montana. A rancher nearby, the book says, called them “larger than milk pans” and measured one at 15 inches wide. But no corroborating evidence supports the claim.

“Who of us has seen a hailstone the size of a golf ball or a baseball?” asked Kenneth G. Libbrecht, a snowflake devotee at the California Institute of Technology who runs the physics department there in his spare time. “But, clearly, they exist, because people pull them out of their freezers. Some of these things can be very, very rare, but not impossible.”