How Is Rainfall Measured?

How is rainfall measured? What does it mean when it rains an inch? And how many gallons of water fall on your roof in a storm? Keep on reading to learn all about the math behind April showers and May flowers.

Jason Marshall, PhD,
February 12, 2016
Episode #196

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How to Make a More Accurate Rain Gauge

As it turns out, straight-sided cans aren't very accurate since small amounts of rain don't change the water level much. One simple way to improve the accuracy of this kind of rain gauge is to use a funnel shaped collector instead of one with straight-sides. The large mouth at the top of the funnel gathers lots of rain and the narrow tube at the bottom means that even a small amount of rain changes the height of the water significantly.

Of course, with this kind of collector 1 inch of water in the gauge does not mean 1 inch of rainfall. Real rain gauges of this type have nice markings on them that let you to accurately tell how much it has rained, but you don't actually need those markings to find out. As we talked about earlier for the straight-sided gauge, the number of inches of rain must be equal to the volume of water divided by the area of the collector. So, by measuring the volume and area, you can determine the number of inches of rain. And you can actually use this technique to determine how the scale should be drawn on your rain gauge in the first place.

How Much Rain Falls On Your Roof?

So how much is 1 inch of rain? By which I mean something like: How many gallons of water land on your roof in a storm that drops 1 inch of rain? The math is actually pretty straightforward—although there are some unit conversions that we need to be careful about along the way.

A 1,000 square foot roof is bombarded by 625 gallons of water per inch of rain.

The main thing to realize is that 1 inch of rainfall is enough to create a 1 inch deep layer of water on your roof. So the total volume of water on your roof is the square footage of your roof—let's say it's 1,000 square feet—times 1 inch = 1/12 of a foot. That's about 83.3 cubic feet of water per inch of rain for a 1,000 square foot roof. How many gallons is that?

There are just about 7.5 gallons in a cubic foot. Which means that a 1,000 square foot roof is bombarded by 83.3 x 7.5 or about 625 gallons of water per inch of rain. How much is that? Well, a typical barrel shaped container used to transport liquids holds 55 gallons. So if you could collect all of that water, you could fill almost 11.5 barrels from a single inch of rain. That's a lot of water!

Wrap Up

OK, that's all the math we have time for today.

Please be sure to check out my book The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Red umbrella and rain gauge images from Shutterstock.


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