Solid angle

angular areasolid angles4-πsquare minutesquare second
In geometry, a solid angle (symbol:wikipedia
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Field of view

FOVfields of viewwide-field
) is a measure of the amount of the field of view from some particular point that a given object covers.
In the case of optical instruments or sensors it is a solid angle through which a detector is sensitive to electromagnetic radiation.

Steradian

srsteradiansmillisteradians
In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr).
The steradian (symbol: sr) or square radian is the SI unit of solid angle.

Square degree

deg 2 square degreesdeg2
Solid angles can also be measured in squares of angular measures such as degrees, minutes, and seconds. The solid angle of a sphere measured from any point in its interior is 4[[Pi|]] sr, and the solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2⁄3 sr. Solid angles can also be measured in square degrees (1 sr = (1⁄180) 2 square degrees), in square minutes and square seconds, or in fractions of the sphere (1 sr = 1⁄4 fractional area), also known as spat (1 sp = 4 sr).
A square degree (deg 2 ) is a non-SI-compliant unit measure of solid angle.

International System of Units

SISI unitsSI unit
In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr).

Radian

radiansradmicroradian
A solid angle in steradians equals the area of a segment of a unit sphere in the same way a planar angle in radians equals the length of an arc of a unit circle; therefore, just like a planar angle in radians is the ratio of the length of a circular arc to its radius, a solid angle in steradians is the following ratio:
Separately, the SI unit of solid angle measurement is the steradian.

Spat (unit)

spat
The solid angle of a sphere measured from any point in its interior is 4[[Pi|]] sr, and the solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2⁄3 sr. Solid angles can also be measured in square degrees (1 sr = (1⁄180) 2 square degrees), in square minutes and square seconds, or in fractions of the sphere (1 sr = 1⁄4 fractional area), also known as spat (1 sp = 4 sr).
The spat (symbol sp ), from the Latin spatium ("space"), is a unit of solid angle.

Luminance

cd/m 2 brightnessluminous
Defining luminous intensity and luminance, and the correspondent radiometric quantities radiant intensity and radiance
It describes the amount of light that passes through, is emitted or reflected from a particular area, and falls within a given solid angle.

Radiance

spectral radianceintensitybrightness
Defining luminous intensity and luminance, and the correspondent radiometric quantities radiant intensity and radiance
In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area.

Luminous intensity

intensityluminouslight intensity
Defining luminous intensity and luminance, and the correspondent radiometric quantities radiant intensity and radiance
In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye.

Radiant intensity

intensityradiation intensityphoton intensity
Defining luminous intensity and luminance, and the correspondent radiometric quantities radiant intensity and radiance
In radiometry, radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and spectral intensity is the radiant intensity per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength.

Ligand cone angle

cone angleTolman cone anglesmall
Evaluating the size of ligands in metal complexes, see ligand cone angle
It is defined as the solid angle formed with the metal at the vertex and the outermost edge of the van der Waals spheres of the ligand atoms at the perimeter of the cone (see figure).

Earth

terrestrialworldGlobal
For example, although the Moon is much smaller than the Sun, it is also much closer to Earth.
The angular size (or solid angle) of these two bodies match because, although the Sun's diameter is about 400 times as large as the Moon's, it is also 400 times more distant.

Angle

acute angleacuteoblique
A solid angle in steradians equals the area of a segment of a unit sphere in the same way a planar angle in radians equals the length of an arc of a unit circle; therefore, just like a planar angle in radians is the ratio of the length of a circular arc to its radius, a solid angle in steradians is the following ratio:
Solid angle for a concept of angle in three dimensions.

Tetrahedron

tetrahedraltetrahedra{3,3}
Let OABC be the vertices of a tetrahedron with an origin at O subtended by the triangular face ABC where are the vector positions of the vertices A, B and C. Define the vertex angle to be the angle BOC and define, correspondingly.

Angular diameter

apparent diameterangular sizeapparent size
The Sun is seen from Earth at an average angular diameter of 0.5334 degrees or 9.310 radians.
(Sirius has twice the diameter and its distance is 500,000 times as much; the Sun is 10 10 times as bright, corresponding to an angular diameter ratio of 10 5, so Sirius is roughly 6 times as bright per unit solid angle.)

Spherical coordinate system

spherical coordinatessphericalspherical polar coordinates
In spherical coordinates there is a formula for the differential,
Thus the differential solid angle is

Spherical cap

DomeHemispherical
, is the area of a spherical cap on a unit sphere
Solid angle — contains formula for n-sphere caps

Sphere

sphericalhemisphereglobose
where the surface area of a sphere is
Solid angle

Geometry

geometricgeometricalgeometries
In geometry, a solid angle (symbol:

Subtended angle

subtendedsubtendsubtends
The point from which the object is viewed is called the apex of the solid angle, and the object is said to subtend its solid angle from that point.

Dimensionless quantity

dimensionlessdimensionless numberdimensionless quantities
In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr).

Unit of measurement

unitunits of measurementunits
In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr).

Unit sphere

unit ballclosed unit ballsphere
, is the area of a spherical cap on a unit sphere One steradian corresponds to one unit of area on the unit sphere surrounding the apex, so an object that blocks all rays from the apex would cover a number of steradians equal to the total surface area of the unit sphere, 4\pi.

Surface area

SurfaceAreafootprint
One steradian corresponds to one unit of area on the unit sphere surrounding the apex, so an object that blocks all rays from the apex would cover a number of steradians equal to the total surface area of the unit sphere, 4\pi.

Moon

lunarthe MoonLuna
For example, although the Moon is much smaller than the Sun, it is also much closer to Earth.