# Square degree

Physical unit
Unit name Square degree
Unit symbol ${\ displaystyle \ mathrm {deg ^ {2}}}$ , ,${\ displaystyle \ mathrm {sq.deg.}}$ ${\ displaystyle \ mathrm {(^ {\ circ}) ^ {2}}}$ Physical quantity (s) Solid angle
Formula symbol ${\ displaystyle \ Omega}$ dimension ${\ displaystyle {\ mathsf {{\ frac {L ^ {2}} {L ^ {2}}} = 1}}}$ In SI units ${\ displaystyle \ mathrm {1 \ deg ^ {2} = {\ frac {\ pi ^ {2}} {32 \, 400}} \; sr}}$ Square degrees ( deg² , (°) ² ) ( English square degree or sq degree ) is a (non-legal) unit for the solid angle . It is mainly used in astronomy as a measure of the extent of an object in the sky .

The sub-units are called accordingly:

• Square arc minute ( English square arcmin )  square degrees${\ displaystyle = {\ frac {1} {3600}}}$ • Square arcsecond ( English square arcsec )  square minute  square degrees.${\ displaystyle = {\ frac {1} {3600}}}$ ${\ displaystyle = {\ frac {1} {12 \, 960 \, 000}}}$ The full solid angle of the celestial sphere is sr =${\ displaystyle 4 \ pi}$ ${\ displaystyle {\ frac {(360 \ \ mathrm {deg}) ^ {2}} {\ pi}} \ approx 41 \, 253 \ \ mathrm {deg ^ {2}}}$ The size of a celestial object in square degrees results from the proportion of the celestial sphere that the object covers, multiplied by 41253.

The conversion of a square degree into steradian results in:

{\ displaystyle {\ begin {aligned} \ Leftrightarrow 1 \ \ mathrm {deg} ^ {2} & = \ left ({\ frac {2 \ pi} {360}} \ right) ^ {2} \ \ mathrm { sr} \\ & = \ left ({\ frac {\ pi} {180}} \ right) ^ {2} \ \ mathrm {sr} \\ & = {\ frac {\ pi ^ {2}} {32 \, 400}} \ \ mathrm {sr} \\ & \ approx 3 {,} 0461741 \ cdot 10 ^ {- 4} \ \ mathrm {sr} \\ & \ approx 0 {,} 00030461741 \ \ mathrm {sr } \ end {aligned}}} or.

${\ displaystyle \ Leftrightarrow 1 \ \ mathrm {sr} \ approx 3283 \ \ mathrm {deg} ^ {2}}$ For small angles , solid angles can be calculated approximately as with surfaces: an object whose extension measures 1 degree in one direction and 1 degree perpendicular to it, therefore covers a solid angle of around 1 square degree.