Square degree

An illustration of a solid angle formed by a rectangular pyramid, whose apex angles are both 10 degrees. The resulting solid angle is about Template:Val square degrees. The size of Moon, as seen from Earth, is shown in yellow for comparison.

A square degree (deg²) is a non-SI unit measure of solid angle. Other denotations include sq. deg. and (°)². Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere.

Analogous to one degree being equal to Template:Sfrac radians, a square degree is equal to (Template:Sfrac)² steradians (sr), or about Template:Sfrac sr or about Template:Val (millisteradian). The whole sphere has a solid angle of Template:Val, which is approximately Template:Val:

$4\pi {\left(\frac{180}{\pi }\right)}^2{\mathrm{deg}}^2=\frac{360^2}{\pi }{\mathrm{deg}}^2=\frac{129600}{\pi }{\mathrm{deg}}^2\approx 41252.96{\mathrm{deg}}^2.$

Subdivisions

Each square degree is equal to 3600 square arcminutes, and each square arcminute is equal to 3600 square arcseconds. So, each square degree is equal to Template:Val square arcseconds. The whole sphere contains about 148.51 million square arcminutes and about 534.64 billion square arcseconds.

Examples

• The full moon covers only about Template:Val of the sky when viewed from the surface of the Earth. The Moon is only a half degree across (i.e. a circular diameter of roughly Template:Val), so the moon's disk covers a circular area of Template:Pi(Template:Sfrac)², or Template:Val. The moon varies from 0.188 to Template:Val depending on its distance from the Earth.
• Viewed from Earth, the Sun is roughly half a degree across (the same as the full moon) and covers only Template:Val as well.
• It would take Template:Gaps times the full moon (or the Sun) to cover the entire celestial sphere.
• Conversely, an average full moon (or the Sun) covers the fraction 2 / Template:Val, or less than 1/1000 of a percent (Template:Val) of the celestial hemisphere, or above-the-horizon sky.
• Assuming the Earth to be a sphere with a surface area of 510 million square kilometres, the area of Northern Ireland (Template:Val) represents a solid angle of Template:Val, Connecticut (Template:Val) represents a solid angle of Template:Val, and Equatorial Guinea (Template:Val) represents a solid angle of Template:Val.
• The largest constellation, Hydra, covers a solid angle of Template:Val, whereas the smallest, Crux, covers only Template:Val.

See also

• Steradian
• Spat (angular unit)
• Minute and second of arc
• List of constellations by area

External links

• Template:Cite web