The most common solar units:

1. solar mass M_☉ = 1.98855(25)*10**30 kg: For main-sequence stars (i.e., those hydrogen burning in their cores), the stellar mass range is ∼ 0.075--315 M_☉ (see Wikipedia: Stellar mass: Range; Wikipedia: Red dwarf: Description and characteristics; Wikipedia: R136a1).
2. solar luminosity L_☉ = 3.846*10**26 W: For main-sequence stars, the luminosity range is ∼ 0.0015--10**6 L_☉ (see Wikipedia: Red dwarf: Description and characteristics; Wikipedia; O-type main-sequence star).
3. solar radius R_☉ = 6.957*10**5 km = 109.1 R_eq_⊕ = 4.650*10**(-3) AU: For main-sequence stars, stellar radius range is ∼ 0.08--10 R_☉ (see Wikipedia: Red dwarf: Description and characteristics; Wikipedia; O-type main-sequence star: Properties). Red supergiants can be much larger: up to over 1000 R_☉ = 4.650 AU (Red supergiant star: Properties).
4. solar composition: Fiducial mass fraction values 0.73 hydrogen H; 0.25 helium (He); 0.02 metallicity Z. Note, the term solar composition can mean either the composition of the present-day solar photosphere (solar radius R_☉ = 6.957*10**5 km = 109.1 R_eq_⊕ = 4.650*10**(-3) AU) or the composition primordial solar nebula which is the most used meaning because of its greater importance for the formation and evolution of the Solar System. The fiducial values apply to both meanings. Best values circa 2021 for the primordial solar nebula: 0.7121 hydrogen H; 0.2725 helium (He); 0.0154 metallicity Z (Asplund et al. 2021, The chemical make-up of the Sun: A 2020 vision, p. 22; see also, Wikipedia: Metallicity: Mass fraction). See also Solar System file: solar_composition.html for a plot of the primordial solar nebula composition. The solar composition is to 1st order the modern cosmic composition, except that the metallicity Z (by mass fraction) varies from ∼ 10**(-6) (for extreme Population II stars: e.g., Caffau's star (AKA SDSS J102915+172927): see spectrum plot star_caffau.html) to over 0.01--0.02 which is similar to the fiducial solar composition value 0.02.

Less common solar units:

1. mean solar density ρ_☉ = 1.408 g/cm**3 >∼ ρ_water_fiducial = 1 g/cm**3: Note the Sun density varies extremely (∼ 150 g/cm**3 at the center; ∼ 3*10**(-7) g/cm**3 at the solar photosphere), and so the mean solar density is NOT a good overall characteristic density for the Sun (see Wikipedia: Sun: Core; Wikipedia: Photosphere: Sun). Other stars also have extreme density variation, and so in general there is NO good overall characteristic density for stars.
2. solar effective temperature T_eff_☉ = 5777 K: Note effective temperature varies extremely for stars, and so there is NO good general characteristic effective temperature for stars.

In fact, the solar units solar mass M_☉ and solar luminosity L_☉ are also used for star clusters, galaxies, galaxy clusters, dark halos, etc. This usage is NOT particularly natural because these astronomical objects are much more massive and luminous than stars. However, since their luminous part is largely made of stars, solar units are, in a sense, natural units. The usage also leads to a rough estimation tool: e.g., if there are 10**11 M_☉ in stars, then there are roughly 10**11 stars.

Local file: local link: solar_units.html.
File: Sun file: solar_units.html.