Unit definitions

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 $4\pi\ \text{sr}$.

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 $1\ \text{sr}$.

How to convert Full sphere to Steradian

$$\text{Solid Angle}_{\text{sr}} = \text{Solid Angle}_{\text{4π sr}} \cdot 4 \cdot 3.141592653589793$$

Examples

Example 1

Convert $40.0\ \text{4π sr}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 40.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 502.654825$$

$$\therefore \ 40.0\ \text{4π sr} = 502.654825 \ \text{sr}$$

Example 2

Convert $90.0\ \text{4π sr}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 90.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 1130.973355$$

$$\therefore \ 90.0\ \text{4π sr} = 1130.973355 \ \text{sr}$$

Example 3

Convert $110.0\ \text{4π sr}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 110.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 1382.300768$$

$$\therefore \ 110.0\ \text{4π sr} = 1382.300768 \ \text{sr}$$

Example 4

Convert $145.0\ \text{4π sr}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 145.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 1822.123739$$

$$\therefore \ 145.0\ \text{4π sr} = 1822.123739 \ \text{sr}$$

Example 5

Convert $195.0\ \text{4π sr}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 195.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 2450.44227$$

$$\therefore \ 195.0\ \text{4π sr} = 2450.44227 \ \text{sr}$$

Full sphere to Steradian conversion table

Full sphere to Steradian conversion table

Full sphere [4π sr]	Steradian [sr]
1	12.566371
2	25.132741
3	37.699112
4	50.265482
5	62.831853
6	75.398224
7	87.964594
8	100.530965
9	113.097336
10	125.663706

Convert Full sphere to other Solid Angle units

Convert Full sphere to other Solid Angle units

Full sphere [4π sr]	Other unit
1	1 Spat [sp]