Convert Steradian to Full sphere
Unit definitions
Steradian
The steradian is the SI unit of solid angle. If you take a sphere and mark an area on its surface that has a surface area of $r^2$, where $r$ is the radius of the sphere, then the solid angle formed at the center is $1\ \text{sr}$.
Full sphere
The full sphere represents the solid angle formed at the center of a sphere when the entire surface area of the sphere is considered. It is equal to $4\pi\ \text{sr}$.
How to convert Steradian to Full sphere
$$\text{Solid Angle}_{\text{4π sr}} = \frac{\text{Solid Angle}_{\text{sr}}}{3.141592653589793 \cdot 4}$$
Examples
Example 1
Convert $50.0\ \text{sr}$ to $\text{4π sr}$.
$$\text{Solid Angle}_{\text{4π sr}} = \frac{50.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{4π sr}} = 3.978874$$
$$\therefore \ 50.0\ \text{sr} = 3.978874 \ \text{4π sr}$$
Example 2
Convert $70.0\ \text{sr}$ to $\text{4π sr}$.
$$\text{Solid Angle}_{\text{4π sr}} = \frac{70.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{4π sr}} = 5.570423$$
$$\therefore \ 70.0\ \text{sr} = 5.570423 \ \text{4π sr}$$
Example 3
Convert $100.0\ \text{sr}$ to $\text{4π sr}$.
$$\text{Solid Angle}_{\text{4π sr}} = \frac{100.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{4π sr}} = 7.957747$$
$$\therefore \ 100.0\ \text{sr} = 7.957747 \ \text{4π sr}$$
Example 4
Convert $140.0\ \text{sr}$ to $\text{4π sr}$.
$$\text{Solid Angle}_{\text{4π sr}} = \frac{140.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{4π sr}} = 11.140846$$
$$\therefore \ 140.0\ \text{sr} = 11.140846 \ \text{4π sr}$$
Example 5
Convert $175.0\ \text{sr}$ to $\text{4π sr}$.
$$\text{Solid Angle}_{\text{4π sr}} = \frac{175.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{4π sr}} = 13.926058$$
$$\therefore \ 175.0\ \text{sr} = 13.926058 \ \text{4π sr}$$
Steradian to Full sphere conversion table
Convert Steradian to other Solid Angle units
| Steradian [sr] | Other unit |
|---|---|
| 1 | 0.079577 Spat [sp] |