Measure of how large an object appears to an observer at a given point in three-dimensional space
Not to be confused with spherical angle.
Solid angle
Visual representation of a solid angle
Common symbols
Ω
SI unit
steradian
Other units
Square degree, spat (angular unit)
In SI base units
m2/m2
Conserved?
No
Derivations from other quantities
Dimension
In geometry, a solid angle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point.
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 at that point.
In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr). 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, . Solid angles can also be measured in squares of angular measures such as degrees, minutes, and seconds.
A small object nearby may subtend the same solid angle as a larger object farther away. For example, although the Moon is much smaller than the Sun, it is also much closer to Earth. Indeed, as viewed from any point on Earth, both objects have approximately the same solid angle (and therefore apparent size). This is evident during a solar eclipse.
In geometry, a solidangle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is...
The contact angle (symbol θC) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the...
analog of a plane angle is a solidangle. The solidangle, Ω, at the vertex of a Platonic solid is given in terms of the dihedral angle by Ω = q θ − ( q...
geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed...
from, or is reflected from a particular area, and falls within a given solidangle. The procedure for conversion from spectral radiance to luminance is...
The steradian (symbol: sr) or square radian is the unit of solidangle in the International System of Units (SI). It is used in three dimensional geometry...
radius. Basic topics in solid geometry and stereometry include: incidence of planes and lines dihedral angle and solidangle the cube, cuboid, parallelepiped...
the solidangle the source subtends as seen from the pupil. These definitions must be applied for infinitesimally small "elements" of area and solid angle...
emitted, reflected, transmitted or received by a given surface, per unit solidangle per unit projected area. Radiance is used to characterize diffuse emission...
Luminance, the original meaning of brightness, is the amount of light per solidangle coming from an area, such as the sky. The table below shows the standard...
between two faces sharing the vertex. The angle may be quantified using a single number by the interior solidangle at the vertex (the spherical excess),...
wavelength-weighted power emitted by a light source in a particular direction per unit solidangle, based on the luminosity function, a standardized model of the sensitivity...
International System of Units (SI). It measures luminous power per unit solidangle emitted by a light source in a particular direction. Luminous intensity...
solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle...
given moment. In the case of optical instruments or sensors, it is a solidangle through which a detector is sensitive to electromagnetic radiation. It...
the radiant flux emitted, reflected, transmitted or received, per unit solidangle, and spectral intensity is the radiant intensity per unit frequency or...
ligand cone angle (θ) is a measure of the steric bulk of a ligand in a transition metal coordination complex. It is defined as the solidangle formed with...
tilted at an angle to a source, the illumination provided on the surface is reduced because the tilted surface subtends a smaller solidangle from the source...
by a light source that emits one candela of luminous intensity over a solidangle of one steradian. 1 lm = 1 cd × 1 sr {\displaystyle 1\ {\text{lm}}=1\...
they are ranked by the solidangle that they subtend in the sky, measured in square degrees and millisteradians. These solidangles depend on arbitrary boundaries...
which simply calculates the ratio of the beam solidangle to the solidangle of a sphere. The beam solidangle can be approximated for antennas with one narrow...
\,\mathrm {d} \theta \,\mathrm {d} \varphi ~.} Thus the differential solidangle is d Ω = d S r r 2 = sin θ d θ d φ . {\displaystyle \mathrm {d} \Omega...
A square degree (deg2) is a non-SI unit measure of solidangle. Other denotations include sq. deg. and (°)2. Just as degrees are used to measure parts...
Created in Spain by Marcos Fajardo and later co-developed by his company SolidAngle SL (now owned by Autodesk) and Sony Pictures Imageworks, Arnold is one...
where Ω is the solidangle of the spherical sector in steradians, the SI unit of solidangle. One steradian is defined as the solidangle subtended by a...
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