When Pope Francis dropped his latest pro-environment encyclical earlier in June, his papal thunderstrike thwacked climate-change denialism and social media use as well. What he didn’t do was connect the two. Most people don’t, presumably because, on the environmental damage scale from stepping on a twig to operating a container ship, sharing a Snapchat registers next to blowing on a dandelion. However, the impact is not zero. To paraphrase economist Milton Friedman, there’s no such thing as free lunch or a free self-destructive information packet.

To estimate a single Snapchat’s carbon footprint, we first have to determine the energy it takes to share a hypothetical Snapchat image or video. Every time someone uploads an image from his or her phone, the data travels through a knot of routers and switches. A well-honed paper by researchers at the University of Melbourne’s Centre for Energy-Efficient Telecommunications in 2014 attempts to untangle that web. They mapped out sharing a Facebook photo, which we’ll use as a guide to Snapchat.

The upload energy consumption of a phone on a 4G network was 40 Joules for a 5 MB Facebook photo, which, assuming a linear relationship between energy and data size, gives us 24 Joules for our Snapchat. (We’ll also assume the snap we’ve chatted is the maximum file size of 3MB.) On the download end, it’s 10.8 Joules for a 3 MB file, as there’s less observed data traffic after the files get compressed. Our phones are covered. Next up: The immediate destination, a cellular LTE base station tower. That’s 402 Joules to upload, 10.8 Joules for a download, extrapolating from the Melbourne researchers’ Facebook calculations.

From there, our Snapchat Odysseus traverses the core network comprising large core routers and optical links.The final destination for storing photos is a physical disk drive inside a data center (computer clouds are indeed physical). Again, the way Facebook operates is likely different from Snapchat — depending on the file or geographical location, Facebook might use an older Akamai server or its data center, whereas Snapchat uses Google App Engine. (But we’ll make do with these Facebook estimates because Snapchat declines to comment about the energy sourcing or server efficiency.) Uploading and downloading from a data center, based on the paper, requires roughly 1.2 Joules.

The total energy consumed over the course of the Snapchat, in a very liberal approximation, is about 450 Joules. The biggest energy consumer is the base station, and the authors note the greatest gains in greener social media “would come from improving the energy-efficiency of the access network, especially for wireless 3G/4G/LTE.”

What does 450 Joules of energy consumed look like in terms of a carbon footprint? Again, this is hard to pin down authoritatively; it depends on the source of the energy that powers the machines along the way. Even “carbon footprint,” as a term, is shorthand for the warming impact an action might have. Approximations are possible, however. Using the Environmental Protection Agency’s calculator, the energy consumed by our Snapchat yields the greenhouse equivalent of 0.1 grams of carbon dioxide.

It would take about 55 million Snapchats to produce the carbon dioxide equivalent of driving a car for one year. That seems huge, until you discover the number of Snapchats received per day. If 2013 company numbers are to be believed (don’t take them as gospel)), that’s seven years of driving a day. It’s not a massive carbon footprint, but it ain’t nothing either.

The Pope wouldn’t be pleased.

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