# Steradian

**steradian**(steradian, symbol: sr) is a unit in (SI). Correspond to. There is another one in solid angle unit.

Steradian steradian - - Symbol | sr | (SI) Type | | Solid angle Assembly | / m2 Definition | solid angle relative to the center of the part on the spherical surface equal to the square of the sphere Etymology | στερεός (stereos; entity, solid) + radius (radius)

## table of contents

Overview

1 steradian is equal to the square of r (the radius of the sphere is taken as the length of one side) of a part a on the spherical surface a The solid angle with respect to the center [sr]. The steradian is an extension of the plane angular radians to a solid.

[\ \ displaystyle \ left \ [\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ mathrm {sr} \ right ] = {\ \ frac {a} {r ^ {2}}.}] (https://wikimedia.org/api/rest_v1/media/math/render/svg/ fe80 f3360102fac095e6b2a5b75607fc06390c98)

Although there is a unit for "SI", only the steradian is recognized for the solid angle, whereas the degree is a combination unit in SI.

The name "steradian" was used from about 1875, and it is called *stereos* (Also the etymology of). The steradian was the 11th CGPM in 1960 Was adopted. It was supposed to be one of SI along with radians, but in 1995 the subsidiary unit was abolished and steradian became dimension 1 (= m2 ⋅ m - 2), ie dimensionless.

From the definition of steradians, the global (area 4 _ π r - 2) is 4 _ π _ steradian (= about 12.566 steradian), the hemisphere is 2 π _ It becomes steradian (= about 6.2832 steradian). Conversely, 1 steradian is 1/4 _ π = about 0.079577 .

The solid angle (steradian) of the cone with half apex angle θ is

2 _ [pi] _ (1 - cos _ [theta] _)

, And the solid angle (steradian) in the range surrounded by latitude *δ* 1 to _δ _ 2 (radian), longitude _λ _ 1 to _λ _ 2 (radian)

{\ displaystyle \ left (\ sin \ delta _ {2} - \ sin \ delta _ {1} \ right) \ left (\ lambda _ sin __ 2 - sin δ 1) {2} - \ lambda _ {1} \ right)}! \ \ Left \ (\ sin \ delta _ {2} - \ sin \ delta _ {1} \ right ) \ left \ (\ lambda _ {2} - \ lambda _ {1} \ right )] (https://wikimedia.org/api/rest_v1/media/math/render/svg/84f6b8e6f623dc30d37b0025302ae1ef351c027c)

.

Relationship with squared degree

The relationship with the other unit of solid angle (deg 2) is as follows.

- 1 sr = about 3282.806350012 deg 2
- 1 deg 2 = about 0.00030461741979 sr

application

Stellarian is often used for measurement of.

Etc. are radiated equal in all directions under certain conditions. Under such conditions, the radiant flux per unit area weakens farther from the light source, but the radiant flux per unit solid angle becomes constant irrespective of the distance from the light source. Also, even when completely "radiating equally in all directions", the same thing can be said about in approximation (for example: Naked bulbs, red hot iron pieces). This is the reason why steradian is used to measure radiant flux. In SI, there is every steradian (W / sr) in the unit of. It is also a unit of (cd) in watts per steradian appears in the definition.

Code position

Symbol | Name | ||
---|---|---|---|

㏛ | `U + 33 DB` | `-` | ` & # x 33 DB; |

`㏛` | steradian |

The above characters representing steradian are recorded. This is because it is included for backward compatibility with existing character codes, so use is not recommended.

footnote

1. ** *"" (2015). Viewed 21 February 2016. 2. ***"". Mountain View, CA: The Unicode Consortium (2015). Viewed 21 February 2016.

Related item

- *

Acquired from ""

Post Date : 2018-01-25 05:00

This article is taken from the Japanese Wikipedia **Steradian**

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