# Xkcd 03/11/2023

**URL:** <https://boards.straightdope.com/t/xkcd-03-11-2023/981074>\
**Category:** Cafe Society\
**Tags:** comic-strips\
**Created:** [March 12, 2023, 6:02pm UTC](https://boards.straightdope.com/t/xkcd-03-11-2023/981074 "2023-03-12T18:02:14Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\
**Post date:** [March 12, 2023, 6:02pm UTC](https://boards.straightdope.com/t/xkcd-03-11-2023/981074/1 "2023-03-12T18:02:15Z")

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> **[Radians are Cursed](https://xkcd.com/2748/)**
>
> Phil Plait once pointed out that you can calculate the total angular area of the sky this way. If the sky is a sphere with radius 57.3 degrees, then its area is 4\*pi\*r^2=41,253 square degrees. This makes dimensional analysts SO mad, but you can't argue with results.

What’s the joke here? AFAIK radians in fact do allow one to calculate the number of square degrees of sky.

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [March 12, 2023, 6:24pm UTC](https://boards.straightdope.com/t/xkcd-03-11-2023/981074/2 "2023-03-12T18:24:07Z")

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We’re used to talking about angles as measured in degrees, and we’re used to talking about angles as measured in radians, which are considered to actually be dimensionless. It also feels natural to speak of a circle with a dimensionless radius, but even though it follows logically from all of that, it’s still never done to refer to dimensionless quantities other than angles in degrees.

It’s like measuring torque in joules. Sure, you can, and there’s nothing actually invalid about it, but nobody actually does it, and so it just looks wrong.

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<div class="post-metadata">

**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\
**Post date:** [March 12, 2023, 6:28pm UTC](https://boards.straightdope.com/t/xkcd-03-11-2023/981074/3 "2023-03-12T18:28:05Z")

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And yet a sphere _does_ have a surface of approximately 41,253 square degrees. So is it that the example given just isn’t the proper way to go about it, or what?

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [March 12, 2023, 6:46pm UTC](https://boards.straightdope.com/t/xkcd-03-11-2023/981074/4 "2023-03-12T18:46:56Z")

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> [@Chronos](#):
>
> it follows logically from all of that

Logically, how many degrees would the radius of a _non_-unit circle have?

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<div class="post-metadata">

**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [March 12, 2023, 7:46pm UTC](https://boards.straightdope.com/t/xkcd-03-11-2023/981074/5 "2023-03-12T19:46:53Z")

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Depends on how non-unit it is. A circle of radius 2 would be 114.6 degrees, and so on.

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**Author:** ![Wisest\_Novel](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wisest_novel/32/13329_2.png) [@Wisest\_Novel](https://boards.straightdope.com/u/Wisest_Novel)\
**Post date:** [March 14, 2023, 1:05am UTC](https://boards.straightdope.com/t/xkcd-03-11-2023/981074/6 "2023-03-14T01:05:48Z")

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There’s a site dedicated to working through Randall’s always brilliant, sometimes nebulous comics.[Here’s](https://www.explainxkcd.com/wiki/index.php/2748) the one that treats this comic.