Solid Angles 101: A Crash Course

[kerasene]

Hey I'm having a hard time wrapping my head around the concept of solid angles and finding the solid angle of any area on the surface of a sphere I'm basically asking for a crash course none of my textbooks explain it well at all

 

[mathman]

The most direct way is is the area of the surface patch divided by r², where r is the radius of the sphere.

 

[HallsofIvy]

Mathman is correct. That's how the measure of a solid angle is defined- the "solid angle" intecepted by the entire sphere around a point has measure $4\pi$, the surface area, $4\pi r^2$, divided by $r^2$.