Steradian facts for kids
The steradian (say: STAIR-ray-dee-an) is a special unit of measurement. It's part of the SI system, which is like the world's standard way to measure things. Think of it like a radian, but for 3D shapes, especially round ones like a sphere (a perfect ball).
A steradian helps us measure a "solid angle." Imagine you're looking at a part of a sphere's surface from its very center. The amount of "view" you get is measured in steradians. It's always about one-twelfth of the total surface area of any sphere, no matter how big or small the sphere is!
What is a Solid Angle?
A solid angle is a bit like a regular angle, but in 3D. A normal angle measures how wide something is on a flat surface. A solid angle measures how much of your view a 3D object takes up. It's like looking at a cone shape, where the tip of the cone is at the center of a sphere, and the wide part of the cone cuts out a piece of the sphere's surface.
Steradians and Spheres
Let's compare how we measure the surface of a sphere and a steradian:
- The total surface area of a sphere is found using the formula:
. Here, 'r' is the radius (the distance from the center to the edge) of the sphere. - The surface area of just one steradian on that sphere is simply
.
This means that a whole sphere measures exactly 4π (four times pi) steradians. Since pi (π) is about 3.14, a sphere is roughly 4 × 3.14 = 12.56 or 12.57 steradians.
So, one steradian is about 1/12.57 of a sphere, which is around 8% of the sphere's total surface. The cool thing is, because we are measuring an angle (how much of your view it takes up), the actual size of the sphere doesn't change how many steradians it has. A tiny marble and a giant planet both have 4π steradians in total!
See also
- In Spanish: Estereorradián para niños
