Sipping Along The Tube

In the US

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, we measure fuel economy in miles/gallon—which could just as easily be written as gallons/mile. (This reciprocal form has some advantages. It’s popular in Europe, where it’s expressed as liters per 100 kilometers.)

But regardless of which units you use, there’s something strange going on here. Miles are units of length, and gallons are volume—which is L3. So gallons/mile is L3 / L, which is L2.

Gas mileage is measured in square meters.

You can even plug it into Wolfram|Alpha, and it’ll tell you that 20 MPG is about 0.1 square millimeters (roughly the area of two pixels on a computer screen).

Unit cancellation is weird.

Ok, so what’s the physical interpretation of that number? Is there one?

It turns out there is! If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.