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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 .
The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A /2 and r = 1 . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ , is the area of a spherical cap on a unit sphere
watt per steradian per square metre per hertz W⋅sr −1 ⋅m −2 ⋅Hz −1: M⋅T −2: Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr −1 ⋅m −2 ⋅nm −1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". L e,Ω,λ [nb 4]
watt per steradian per hertz W⋅sr −1 ⋅Hz −1: M⋅L 2 ⋅T −2: Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr −1 ⋅nm −1. This is a directional quantity. I e,Ω,λ [nb 4] watt per steradian per metre W⋅sr −1 ⋅m −1: M⋅L⋅T −3: Radiance: L e,Ω [nb 5] watt per steradian per ...
Analogous to one degree being equal to π / 180 radians, a square degree is equal to ( π / 180 ) 2 steradians (sr), or about 1 / 3283 sr or about 3.046 × 10 −4 sr. The whole sphere has a solid angle of 4 π sr which is approximately 41 253 deg 2 :
The lumen is defined as equivalent to one candela-steradian (symbol cd·sr): 1 lm = 1 cd·sr. A full sphere has a solid angle of 4π steradians (≈ 12.56637 sr), so an isotropic light source (that uniformly radiates in all directions) with a luminous intensity of one candela has a total luminous flux of
Luminous intensity, a photometric quantity measured in lumens per steradian (lm/sr), or candela (cd) Irradiance, a radiometric quantity, measured in watts per square meter (W/m 2) Intensity (physics), the name for irradiance used in other branches of physics (W/m 2) Radiance, commonly called "intensity" in astronomy and astrophysics (W·sr −1 ...
If a lamp has a 1 lumen bulb and the optics of the lamp are set up to focus the light evenly into a 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 source would have a luminous intensity of 2 candela.