An angle symbolically has dimension $1$. For consistency in the Units package, angles have the dimension length/length(radius). The SI derived unit of angle is the radian, which is defined as the angle for which the radius equals the arclength.

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, radian[SI] or rev[angle]; or, if the context is indicated as the default, by using only the unit name or symbol, for example, radian or rev.

The units of angle are defined as follows.

A degree is defined as $\frac{\mathrm{\pi }}{180}$ radian.

A minute is defined as $\frac{1}{60}$ degree.

A second is defined as $\frac{1}{60}$ minute.

A revolution is defined as $2\mathrm{\pi }$ radians.

A gon, grade, or grad is defined by the relationship: $100$ grades equals $\frac{\mathrm{\pi }}{2}$ radians.

An angular mil is defined as $\frac{1}{1000}$ radian.

A military mil is defined as $\frac{\mathrm{\pi }}{3200}$ radian.

A circle is defined as $2\mathrm{\pi }$ radians.

A semicircle is defined as $\mathrm{\pi }$ radians.

A quadrant is defined as $\frac{\mathrm{\pi }}{2}$ radians.

A sign is defined as $\frac{\mathrm{\pi }}{6}$ radian.

A point is defined as $\frac{\mathrm{\pi }}{16}$ radian.

An hour is defined as $\frac{\mathrm{\pi }}{12}$ radian.

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

$\mathrm{plane\_angle}$

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

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

$\mathrm{convert}\left(10\,'\mathrm{units}'\,'\mathrm{degrees}'\,'\mathrm{radians}'\right)$

$\frac{\mathrm{\pi }}{18}$