Convert Steradian to Spat
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 $1\ \text{sr}$.
Spat
One full sphere equals one spat. Therefore, a spat equals $4\pi\ \text{sr}$.
How to convert Steradian to Spat
$$\text{Solid Angle}_{\text{sp}} = \frac{\text{Solid Angle}_{\text{sr}}}{3.141592653589793 \cdot 4}$$
Examples
Example 1
Convert $20.0\ \text{sr}$ to $\text{sp}$.
$$\text{Solid Angle}_{\text{sp}} = \frac{20.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{sp}} = 1.591549$$
$$\therefore \ 20.0\ \text{sr} = 1.591549 \ \text{sp}$$
Example 2
Convert $90.0\ \text{sr}$ to $\text{sp}$.
$$\text{Solid Angle}_{\text{sp}} = \frac{90.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{sp}} = 7.161972$$
$$\therefore \ 90.0\ \text{sr} = 7.161972 \ \text{sp}$$
Example 3
Convert $120.0\ \text{sr}$ to $\text{sp}$.
$$\text{Solid Angle}_{\text{sp}} = \frac{120.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{sp}} = 9.549297$$
$$\therefore \ 120.0\ \text{sr} = 9.549297 \ \text{sp}$$
Example 4
Convert $140.0\ \text{sr}$ to $\text{sp}$.
$$\text{Solid Angle}_{\text{sp}} = \frac{140.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{sp}} = 11.140846$$
$$\therefore \ 140.0\ \text{sr} = 11.140846 \ \text{sp}$$
Example 5
Convert $185.0\ \text{sr}$ to $\text{sp}$.
$$\text{Solid Angle}_{\text{sp}} = \frac{185.0}{3.141592653589793 \cdot 4}$$
$$\text{Solid Angle}_{\text{sp}} = 14.721832$$
$$\therefore \ 185.0\ \text{sr} = 14.721832 \ \text{sp}$$
Steradian to Spat conversion table
Convert Steradian to other Solid Angle units
| Steradian [sr] | Other unit |
|---|---|
| 1 | 0.079577 Full sphere [4π sr] |