# Need some help about a Steradian

Hi,

hmm I am just a liitle confused in this Steradian. Now I know that this works only with 3D.

Now a radian is = arc of the size of a radius/radius
So that
2*22/7*r/r = 360'
2*22/7rad = 360'
22/7rad = 180'

Now that's how a radian is counted in 2D
Is there any connection like this in a steradian? I mean can it be converted into degrees and measure the angle of 3D objects.

I just need to know this because I am realy confused of this Steredian. Please guy if you got any links about it post here.

Thanks

## Answers and Replies

Doc Al
Mentor
Just like the 2D angle can be measured using the radius of a circle (1 radian equals the angle subtended by an arc length of 1 radius), so can the 3D solid angle: 1 steradian equals the solid angle subtended by an area of one radius squared on the surface of a sphere.

http://www.usd.edu/~schieber/trb2000/sld021.htm [Broken]
http://en.wikipedia.org/wiki/Steradian

Last edited by a moderator:
Meir Achuz
Science Advisor
Homework Helper
Gold Member
Degrees only work for angles where 180 degrees=pi radians.
Degrees do not connect to steradians.
An entire sphere covers 4pi steradians.
Just forget about degrees and steradians are easy.

Oh that's right

So steradians do not connect with degrees?
I see. But then in what unit do they measure the angle. Is it just Steredian and then make the sums.

Meir Achuz
Science Advisor
Homework Helper
Gold Member
The unit is "steradian". For instance, a hemisphere has 2\pi steradians.

SpaceTiger
Staff Emeritus
Science Advisor
Gold Member
Well, they might not be able to forget entirely about degrees. In astronomy, for example, angular areas are often quoted in "square degrees". Converting is just a matter of multiplying by the square of the conversion from radians to degrees:

Angular Area of sphere = $4\pi$ steradians = $4\pi(\frac{360}{2\pi})^2$ square degrees $\simeq$ 41,000 square degrees

The important thing to remember is that it's a unit of angle squared. Conversion should then be easy.

hey thanks that's very useful. Thanks alot