A graphical representation of two different steradians. The sphere has radius r, and in this case the area A of the highlighted spherical cap is r2. The solid angle Ω equals [A/r2] sr which is 1 sr in this example. The entire sphere has a solid angle of 4π sr.
General information
Unit system
SI
Unit of
solid angle
Symbol
sr
Conversions
1 sr in ...
... is equal to ...
SI base units
1 m2/m2
square degrees
32400/π2 deg2 ≈ 3282.8 deg2
The steradian (symbol: sr) or square radian[1][2] is the unit of solid angle in the International System of Units (SI). It is used in three dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians, projected onto a circle, gives a length of a circular arc on the circumference, a solid angle in steradians, projected onto a sphere, gives the area of a spherical cap on the surface. The name is derived from the Greek στερεόςstereos 'solid' + radian.
The steradian is a dimensionless unit, the quotient of the area subtended and the square of its distance from the centre. Both the numerator and denominator of this ratio have dimension length squared (i.e. L2/L2 = 1, dimensionless). It is useful, however, to distinguish between dimensionless quantities of a different kind, such as the radian (a ratio of quantities of dimension length), so the symbol "sr" is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian (W⋅sr−1). The steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit.
Solid angle of countries and other entities relative to the Earth.
^Stutzman, Warren L; Thiele, Gary A (2012-05-22). Antenna Theory and Design. ISBN 978-0-470-57664-9.
^Woolard, Edgar (2012-12-02). Spherical Astronomy. ISBN 978-0-323-14912-9.
The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three dimensional geometry...
quantity measured in watts per steradian (W/sr) Luminous intensity, a photometric quantity measured in lumens per steradian (lm/sr), or candela (cd) Irradiance...
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...
radiant intensity is the watt per steradian (W/sr), while that of spectral intensity in frequency is the watt per steradian per hertz (W·sr−1·Hz−1) and that...
which includes two dimensionless derived units, the radian (rad) and the steradian (sr). Some other units such as the hour, litre, tonne, bar, and electronvolt...
unit except the coulomb, ohm, siemens, weber, gray, sievert, radian, and steradian have values that are implicitly defined by the properties of the caesium-133...
1 steradian beam, then the beam would have a luminous intensity of 1 candela. If the optics were changed to concentrate the beam into 1/2 steradian then...
the watt per steradian per square metre per hertz (W·sr−1·m−2·Hz−1) and that of spectral radiance in wavelength is the watt per steradian per square metre...
neutrinos and other particles. The SI unit of radiance is the watt per steradian per square metre (W·sr−1·m−2). It is a directional quantity: the radiance...
that emits one candela of luminous intensity over a solid angle of one steradian. 1 lm = 1 cd × 1 sr {\displaystyle 1\ {\text{lm}}=1\ {\text{cd}}\times...
and the radian was classified as a "supplementary unit" along with the steradian. This special class was officially regarded "either as base units or as...
1700 lumens; if that light is radiated equally in all directions (i.e. over 4π steradians), it will have an intensity of I V = 1700 lm 4 π sr ≈ 135 lm / sr...
directional quantity. Ie,Ω,λ watt per steradian per metre W⋅sr−1⋅m−1 M⋅L⋅T−3 Radiance Le,Ω watt per steradian per square metre W⋅sr−1⋅m−2 M⋅T−3 Radiant...
directional quantity. Ie,Ω,λ watt per steradian per metre W⋅sr−1⋅m−1 M⋅L⋅T−3 Radiance Le,Ω watt per steradian per square metre W⋅sr−1⋅m−2 M⋅T−3 Radiant...
Φv lumen (= candela steradian) lm (= cd⋅sr) J Luminous energy per unit time Luminous intensity Iv candela (= lumen per steradian) cd (= lm/sr) J Luminous...
Photon intensity I count per steradian per second sr−1⋅s−1 T−1 dn/dω Photon radiance Lq count per square metre per steradian per second m−2⋅sr−1⋅s−1 L−2⋅T−1...
dimensionless quantities in the SI. For some relations, their units radian and steradian can be written explicitly to emphasize the fact that the quantity involves...
far-infrared (FIR) maps from the IRAS satellite are in megajanskys per steradian (MJy⋅sr−1). Although extended sources at all wavelengths can be reported...
second is the mole, and only two of the 22 named derived units, radian and steradian, do not depend on the second either. A set of atomic clocks throughout...
special names and symbols as shown in the table below. The radian and steradian have no base units but are treated as derived units for historical reasons...
reciprocal second (1 s−1). The radian (rad) is equal to one (1). The steradian (sr) is equal to one (1). The newton (N) is equal to one kilogram-metre...
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