## How many degrees in a sphere?

**Moderators:** gmalivuk, Moderators General, Prelates

### How many degrees in a sphere?

I know there are 360 degrees in a circle. How many are in a sphere? And can you explain it please. Everyone I asked has said 360 degrees in a sphere, but it just doesn't make sense to me. A circle is 2D, a sphere is 3D. Adding that third dimension makes me think it would have more degrees because there is more to it. Help

### Re: How many degrees in a sphere?

This signature is Y2K compliant.

Last updated 6/29/108

Last updated 6/29/108

### Re: How many degrees in a sphere?

Assume the constant is 1. To obtain the solid angle in steradians, multiply the fractional area by 4*pi. If I want the whole sphere, the fractional area would be 1? So 4*pi = 12.56637 steradians. So there are 4*pi steradians in a sphere, like there are 360 degrees in a circle?

- Cosmologicon
**Posts:**1806**Joined:**Sat Nov 25, 2006 9:47 am UTC**Location:**Cambridge MA USA-
**Contact:**

### Re: How many degrees in a sphere?

Yep, 4pi steradians, and 129,600/pi = 41,252.961... square degrees.

### Re: How many degrees in a sphere?

Thank you and thank math. Things make sense again.

### Re: How many degrees in a sphere?

Bear in mind that 360 degrees in a circle is a very arbitrary labelling. 2Pi radians in a circle is slightly less arbitrary and tends to get used more often as you continue learning maths.

- Cosmologicon
**Posts:**1806**Joined:**Sat Nov 25, 2006 9:47 am UTC**Location:**Cambridge MA USA-
**Contact:**

### Re: How many degrees in a sphere?

True, but I can tell you that square degrees get used a heck of a lot more than steradians in astronomy when referring to a field of view, although the latter do come up every now and again (eg. the Pan-STARRs 3pi steradian survey). I don't know who all uses solid angles very often, but I'm sure astronomers must account for a huge fraction thereof.

### Re: How many degrees in a sphere?

I can't wait for CNN's Anderson Cooper AC41,252.961

"In short, I'm afraid it's not a very surprising or useful thing that you've discovered. Better luck next time!"

### Re: How many degrees in a sphere?

Cosmologicon wrote:True, but I can tell you that square degrees get used a heck of a lot more than steradians in astronomy when referring to a field of view, although the latter do come up every now and again (eg. the Pan-STARRs 3pi steradian survey). I don't know who all uses solid angles very often, but I'm sure astronomers must account for a huge fraction thereof.

Lighting designers - the luminous intensity of a light source is measured in lumens (light output) per steradian.

I've totally pimped your phone, girlfriend!

### Re: How many degrees in a sphere?

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

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

### Re: How many degrees in a sphere?

cheo wrote: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

Area typically has dimensions of length squared, and volume is length cubed. Since angles are effectively dimensionless, I'm confused what you are actually calculating here.

### Re: How many degrees in a sphere?

cyanyoshi wrote:cheo wrote: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

Area typically has dimensions of length squared, and volume is length cubed. Since angles are effectively dimensionless, I'm confused what you are actually calculating here.

A radian is 360/(2pi) = 57.3 degrees, so on a sphere who's radius is 57.3 units long (thus the circumference of a great circle is 360 units), the area of the sphere is 4*pi*r

^{2}= 41,253 units

^{2}.

gmalivuk wrote:Yes. And if wishes were horses, wishing wells would fill up very quickly with drowned horses.King Author wrote:If space (rather, distance) is an illusion, it'd be possible for one meta-me to experience both body's sensory inputs.

- Eebster the Great
**Posts:**3351**Joined:**Mon Nov 10, 2008 12:58 am UTC**Location:**Cleveland, Ohio

### Re: How many degrees in a sphere?

This is definitely the first time I've seen someone try to use degrees cubed. Is there a name for the natural unit of hypersolid angle, where there are like 4π

^{2}of them in a 3-sphere or whatever?### Who is online

Users browsing this forum: No registered users and 5 guests