## How many degrees in a sphere?

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Balkash
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### 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

jmorgan3
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### Re: How many degrees in a sphere?

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

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

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

Thank you and thank math. Things make sense again.

the tree
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### 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
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### 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.

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

I can't wait for CNN's Anderson Cooper AC41,252.961
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Fat Kat
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### 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.
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cheo
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### 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

cyanyoshi
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### 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.

Sizik
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### 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*r2 = 41,253 units2.
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Eebster the Great
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### 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 4π2 of them in a 3-sphere or whatever?

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