On Thursday last week, the Schenectady weather forecast I have in my Bloglines feed called for “Tons of Rain,” which I thought was amusingly unprofessional. I mentioned this to Kate yesterday (after it had, in fact, rained quite a bit), and she said “I wonder how much rain you would need to make a ton?”

Being a physics nerd, of course I had to try to come up with an answer.

We know that one cubic centimeter of water has a mass of one gram, so a (metric) ton of water would be 1,000,000 cubic centimeters, or one cubic meter. Our yard is about 20m x 50m, so if rain covered our yard to a depth of one centimeter (which has happened before), that would amount to about one ton of rain.

Of course, it doesn’t rain just in our yard, and they certainly don’t forecast rain for just our yard. It rains over the whole region, and they do forecasts for the whole region. If you take the region in question to be Schenectady county (as good a choice as any), Wikipedia helpfully tells us that the area of the county is about 543 km^{2}, or 5.4 x 10^{8} m^{2}, so one ton of water would cover that area to a depth of a bit less than 2 nanometers. You wouldn’t even notice the grass being wet.

So, how much rain is a ton of rain? Not much at all. An unimpressive rainstorm, with a tenth of an inch accumulation (the lowest category listed in NASA’s classification) amounts to a bit more than a million tons of rain in Schenectady county alone. (There’s a similar estimate at this blog by a biologist in Minnesota, and not the one you’re thinking of, either.)

The lesson here: Water is really heavy.