# 360 degrees in a Circle. But what about a Sphere? **URL:** \ **Category:** Factual Questions\ **Created:** [June 17, 2003, 12:28am UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341 "2003-06-17T00:28:11Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [June 17, 2003, 3:36pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/21 "2003-06-17T15:36:08Z")
JohnnyLA, I think you’re a pilot, so think of it in terms of navigation. You know that one degree of longitude at the equator is around 60 nautical miles. Also, one degree of latitude is also about 60 nautical miles. So one square degree on the earth’s surface corresponds to about 3600 square nautical miles. So how many square degrees are there on the earth? You can take the number of square nautical miles, and divide by 3600. The radius of the earth is around 3440 nmi, so the surface area is 4\*pi times that: 148,700,000 nmi^2. Dividing by 3600 gives 41,307 square degrees. As you take smaller and smaller angles, the answer will get closer and closer to the 41,253 number that **22/7** gave above. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 17, 2003, 4:49pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/22 "2003-06-17T16:49:35Z")
Bear in mind also that whatever method you come up with for spheres has to work for more general solids. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [June 18, 2003, 12:50am UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/23 "2003-06-18T00:50:32Z")
I get the feeling we’re talking about two different things. Yes, it’s true that at the equator one degree of longitude is 60nm and one degree of latitude covers less distance the farther away from the equator you go. But regardless of the distance it’s still a degree. Suppose you have a globe and designate the north pole as the origin. Arbitrarily set one “great circle” as the prime meridian. Okay, now you can go one degree south and one degree west. Your coordinates from the pole would be 1, -1, right? Okay, you go all the way west and you’ll have 360° around the first degree south of the pole. Now drop down another degree from the pole so that your longitudinal coordinate is -2. Go around the globe at -2 and you get 360 more degrees. And so on. The area covered by the triangle formed between the first degree down, one degree over, and the pole will be different from the area formed by the quadrangle formed by the area between -1 and -2 and 1° west. But it doesn’t matter what the difference is because we’re not talking about area; just the number of whole degrees. So I’m not talking about “square degrees”, but the number of points seperated by one degree on a sphere. Starting from the pole and going to the equator, you have 90 “layers” that are one degree apart. Each of those “layers” have 360 points along its edge that is one degree apart – regardless of the linear distance between them. From the equator to the south pole there are another 90, 360° layers. So do you see what I’m saying? Are we talking about two different things? ---
**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:** [June 18, 2003, 1:24am UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/24 "2003-06-18T01:24:14Z")
When you say that “there are 360 degrees in a circle,” you aren’t really stating a fact about circles, but about degrees: a degree is, by definition, 1/360th of the way around a circle. You can specify exactly where you are on a given circle with only one number (the angle, in degrees or some other unit), but it takes two coordinates to tell where you are on a sphere, so a sphere is a two-dimensional surface (though it lives _in_ three-dimensional space). One way of specifying points on a sphere is by using spherical coordinates (as referred to by **Rabid Squirrel** ), which involve two angles: _theta_, between 0 and 360 degrees, which is like longitude on the Earth’s surface, and _phi_, which ranges from 0 at the north pole, through 90 degrees at the equator, to 180 degrees at the south pole. (A third spherical coordinate, _r_, represents a point’s distance from the origin, but this would be constant for all points on a particular sphere.) ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [June 18, 2003, 1:29am UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/25 "2003-06-18T01:29:48Z")
> [@](#): > > \*Originally posted by Johnny L.A. \* > **So I’m not talking about “square degrees”, but the number of points seperated by one degree on a sphere. Starting from the pole and going to the equator, you have 90 “layers” that are one degree apart. Each of those “layers” have 360 points along its edge that is one degree apart – regardless of the linear distance between them.** We’re using a different definition of “separated by one degree.” You’re dividing the sphere into a 360x360 grid and if you do that, of course you end up with 360x360 grid elements. By that definition, “one degree” is always one grid element. But if you use that definition, if you have an island on the equator 60x60 nautical miles in size it’s 1 square degree, but if the same island were at 60 degree latitude it’ll be 2 square degrees. So this “square degrees” isn’t a useful unit for measuring the “angular area” of an object (i.e. how big a fraction of the entire sphere it occupies). _Solid angle_ is a measure of angular size (angular area, sort of) and must be independent of direction. Solid angle is used to measure things like the field of view of a camera or beam size of a lightbulb - you can’t have the number change just because you pointed the lightbulb at the celestrial north pole. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [June 18, 2003, 12:12pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/26 "2003-06-18T12:12:46Z")
> [@](#): > > But if you use that definition, if you have an island on the equator 60x60 nautical miles in size it’s 1 square degree, but if the same island were at 60 degree latitude it’ll be 2 square degrees. Right. But the question was “how many degrees are there in a sphere?” I took the question literally and visualized global coordinates without regard to the area covered by a set of degrees, and instead just counted points. (Not being a mathematician and not having had any math classes since high school, that’s the only way I _could_ do it. 😉 ) ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [June 18, 2003, 12:15pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/27 "2003-06-18T12:15:38Z")
So. If you look at a globe and count the points one degree apart as I did the previous post, is the answer of 360° in a circle x 180º of latitude = 64,800 one-degree points on a sphere (globe) correct? ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [June 18, 2003, 2:02pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/28 "2003-06-18T14:02:30Z")
Almost correct. If you painted latitude and longitude lines on the earth, one degree apart, they would intersect at 64,442 locations. At latitudes 1 through 179, there would be 360 points each, plus one point each at latitudes 0 and 180: 179\*360+2=64,442. However, I’m not sure why this is useful information. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [June 18, 2003, 4:06pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/29 "2003-06-18T16:06:39Z")
> [@](#): > > \*Originally posted by Johnny L.A. \* > \*\*So. If you look at a globe and count the points one degree apart as I did the previous post, is the answer of 360° in a circle x 180º of latitude = 64,800 one-degree points on a sphere (globe) correct? \*\* Again, we seem to be confusing two definitions of “one degree apart.” Consider two points: [0.0 E, 60.0 N] and [2.0 E, 60.0 N]. If you were looking at a grid pattern on a map, you would call that 2 degrees apart. But imagine drawing a line from each point to the center of the globe and measuring the angle between the two lines; this angle will be 1 degree. Using the latter definition, there are 41,253 points on a sphere which are “one egree apart” from each other. ---
**Author:** ![xash](https://avatars.discourse-cdn.com/v4/letter/x/c6cbf5/32.png) [@xash](https://boards.straightdope.com/u/xash)\ **Post date:** [June 18, 2003, 9:53pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/30 "2003-06-18T21:53:30Z")
Hi. Thanks for all your responses. It will take me a bit to assimilate the information you have provided. I’ll re-read and then re-read again and come back with my doubts, if any. I think the answers from **3\_14159265358979323846** and **Rabid\_Squirrel** was what I was looking for. But I’m not quite sure anymore 🙂 Also, thanks to **scr4** for taking the time to answer **Johnny L.A.**'s questions. If you have further inputs please do add to the discussion. I’ve learnt quite a bit from your answers so far. > [@](#): > > \*Originally posted by DrMatrix \* > \*\*Supplementary answer: There are an infinite number of planes containing the center point. (Im’ not sure what you mean about dividing the sphere into) \*\* I mean it as you correctly understood it… “What is the number of planes that exist that contain the center point of a given sphere” Why is this an infinite figure ? Is it something similar to “How many points on a given line segment” ? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 18, 2003, 10:11pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/31 "2003-06-18T22:11:57Z")
Exactly similar. ---
**Author:** ![cheo](https://avatars.discourse-cdn.com/v4/letter/c/c2a13f/32.png) [@cheo](https://boards.straightdope.com/u/cheo)\ **Post date:** [February 17, 2018, 2:03pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/32 "2018-02-17T14:03:29Z")
what is the volume of a sphere when no dimensions are known? 4pi times radian cubed / 3 = 787,873.524 cubic degrees ---
**Author:** ![cheo](https://avatars.discourse-cdn.com/v4/letter/c/c2a13f/32.png) [@cheo](https://boards.straightdope.com/u/cheo)\ **Post date:** [February 17, 2018, 2:46pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/33 "2018-02-17T14:46:49Z")
360 degrees x 4 x 1/2 Radian = Surface Area of Sphere 41,252 degrees square 41,252 divided by 4 = Area of a Circle in degrees square 10,313.24031 41,252 multipied by 1/3 Radian = Volume of a Sphere in Cubic Degrees 787,873.524 ---
**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:** [February 17, 2018, 2:58pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/34 "2018-02-17T14:58:16Z")
What in the world do you mean by any of that? ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [February 17, 2018, 3:06pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/35 "2018-02-17T15:06:40Z")
And why is it worth pointing out 15 years after the discussion happened? (And why am I still here after 15 years???) ---
**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:** [February 17, 2018, 3:13pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/36 "2018-02-17T15:13:37Z")
I think you have to define “cubic degrees” in terms of hyperspheres. 😃 ---
**Author:** ![Doug\_K](https://avatars.discourse-cdn.com/v4/letter/d/b5ac83/32.png) [@Doug\_K](https://boards.straightdope.com/u/Doug_K)\ **Post date:** [February 17, 2018, 3:22pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/37 "2018-02-17T15:22:55Z")
> [@Chronos](#): > > What in the world do you mean by any of that? Forget it, Chronos, it’s zombietown. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [February 17, 2018, 3:24pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/38 "2018-02-17T15:24:35Z")
Wasn’t **JohnnyLA** actually _in_ LA when he posted here back then? … ---
**Author:** ![Darren\_Garrison](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/darren_garrison/32/92_2.png) [@Darren\_Garrison](https://boards.straightdope.com/u/Darren_Garrison)\ **Post date:** [February 17, 2018, 3:24pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/39 "2018-02-17T15:24:47Z")
Are these cubic degrees Fahrenheit or Celsius? ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [February 17, 2018, 4:11pm UTC](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341/40 "2018-02-17T16:11:17Z")
> [@Darren\_Garrison](#): > > Are these cubic degrees Fahrenheit or Celsius? It’d be -40 in Fahrenheit. Or maybe Celsius. Or possibly kelvins. I forget which. [Previous page](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341.md?page=1) [Next page](https://boards.straightdope.com/t/360-degrees-in-a-circle-but-what-about-a-sphere/182341.md?page=3)