Pie Are Square; Oil Spills Are Round

Ah, not this one again. The folks at Iglu Cruises have put together a helpful infographic to explain various features of the Gulf of Mexico oil spill (via Deep Sea News). Here’s the bit where they compare the recent spill (which, by the way, is still ongoing at a fantastic rate) to previous oil spills. Click for full resolution.

Oil spills: diameter vs. area

Doesn’t make the current fiasco seem so bad, does it? That little blob on the left looks a lot smaller than the blob right next to it, representing Saddam Hussein’s dump of oil into the Persian Gulf during the first Gulf War. In fact, when you think about it, it looks a lot smaller. Which is weird, when you look at the numbers and see that the current spill is 38 million gallons (as of May 27), while the Iraqi spill was 520 million gallons, a factor of about 14 times bigger. The blob representing Iraq’s spill seems a lot more than 14 times the size of the blob for the current spill. You don’t think — no, they couldn’t have done that. Could they?

Yes, they did. When measure the diameter of the circle representing the Iraqi spill, I get about 360 pixels (in the high-res version), while the smaller spill is about 26 pixels — a factor of about 14 larger. But that’s the diameter, not the area. The area of a circle, as many of us learned when we were little, is proportional to the square of its radius: A = π r2. The radius is just half the diameter, so the area is proportional to the diameter squared, not to the diameter. In other words, that big blob is about (14)2 = 196 times the area of the little one, when it should be only 14 times bigger.

I remember reading on some other blog about this same mistake being made in a completely different context, but I have no recollection of where. (Update: it was at Good Math, Bad Math, sensibly enough.) Probably won’t be the last time.

31 Comments

31 thoughts on “Pie Are Square; Oil Spills Are Round”

  1. @Oliver: The values displayed within a pie chart *should* all have the same radius. That takes the area formula out of the picture, so to speak. As long as each slice is allocated a percentage of the pie’s circumference that’s equal to that value’s percentage of the sum, the pie chart will be accurate.

    (I say *should* because I’ve seen pie charts where, oddly enough, some slices of the pie do have a larger radius than other slices. Fortunately, I haven’t seen this recently.)

  2. Current estimates of the Deepwater Horizon oil spill magnitude are more like 630 m barrels, making it the worst U.S. oil spill of all time and the second worst in world history.

    Moreover, unlike the 1991 Gulf War spill, this one isn’t over yet.

  3. @ohwilleke – Ok, I just took a quick glance at the link you posted and the number I am seeing is 630,000 barrels not millions.

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