solid angle - Maple Help

Units of Solid Angle

Description

 • A solid angle symbolically has dimension $1$. For consistency in the Units package, solid angles have the dimension length^2/length(radius)^2. The SI derived unit of angle is the steradian, which is defined as the solid angle for which the surface area equals the radius squared.
 • Maple knows the units of angle listed in the following table.

 Name Symbols Context Alternate Spellings Prefixes steradian sr SI * steradians SI sphere angle * spheres hemisphere angle * hemispheres

 An asterisk ( * ) indicates the default context, an at sign (@) indicates an abbreviation, and under the prefixes column, SI indicates that the unit takes all SI prefixes, IEC indicates that the unit takes IEC prefixes, and SI+ and SI- indicate that the unit takes only positive and negative SI prefixes, respectively.  Refer to a unit in the Units package by indexing the name or symbol with the context, for example, sphere[angle] or sr[SI]; or, if the context is indicated as the default, by using only the unit name or symbol, for example, sphere or sr.
 The units of solid angle are defined as follows.
 A sphere is defined as $4\mathrm{Pi}$ steradians.
 A hemisphere is defined as $2\mathrm{Pi}$ steradians.

Examples

 > $\mathrm{convert}\left('\mathrm{steradian}','\mathrm{dimensions}'\right)$
 ${\mathrm{solid_angle}}$ (1)
 > $\mathrm{convert}\left('\mathrm{steradian}','\mathrm{dimensions}','\mathrm{base}'=\mathrm{true}\right)$
 $\frac{{{\mathrm{length}}}^{{2}}}{{{\mathrm{length}}{}\left({\mathrm{radius}}\right)}^{{2}}}$ (2)
 > $\mathrm{convert}\left(\frac{1}{2},'\mathrm{units}','\mathrm{hemisphere}','\mathrm{steradians}'\right)$
 ${\mathrm{\pi }}$ (3)
 > $\mathrm{convert}\left(3,'\mathrm{units}','\mathrm{steradian}',{'\mathrm{radians}'}^{2}\right)$
 ${3}$ (4)