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.

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.

$\mathrm{convert}\left('\mathrm{steradian}'\,'\mathrm{dimensions}'\right)$

$\mathrm{solid\_angle}$

$\mathrm{convert}\left('\mathrm{steradian}'\,'\mathrm{dimensions}'\,'\mathrm{base}'=\mathrm{true}\right)$

$\frac{{\mathrm{length}}^2}{{\mathrm{length}\left(\mathrm{radius}\right)}^2}$

$\mathrm{convert}\left(\frac{1}{2}\,'\mathrm{units}'\,'\mathrm{hemisphere}'\,'\mathrm{steradians}'\right)$

$\mathrm{\pi }$

$\mathrm{convert}\left(3\,'\mathrm{units}'\,'\mathrm{steradian}'\,{'\mathrm{radians}'}^2\right)$

$3$