- Source: Albers projection
- Albers projection
- Equal-area projection
- Map projection
- Mercator projection
- Lambert conformal conic projection
- Albers
- Gall–Peters projection
- Winkel tripel projection
- AuthaGraph projection
- Mollweide projection
Chapter X (2023)
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Christopher Scott Bradshaw
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The Albers equal-area conic projection, or Albers projection, is a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels. It was first described by Heinrich Christian Albers (1773-1833) in a German geography and astronomy periodical in 1805.
Official adoption
The Albers projection is used by some big countries as "official standard projection" for Census and other applications.
Some "official products" also adopted Albers projection, for example most of the maps in the National Atlas of the United States.
Formulas
= For Sphere
=Snyder describes generating formulae for the projection, as well as the projection's characteristics. Coordinates from a spherical datum can be transformed into Albers equal-area conic projection coordinates with the following formulas, where
R
{\displaystyle {R}}
is the radius,
λ
{\displaystyle \lambda }
is the longitude,
λ
0
{\displaystyle \lambda _{0}}
the reference longitude,
φ
{\displaystyle \varphi }
the latitude,
φ
0
{\displaystyle \varphi _{0}}
the reference latitude and
φ
1
{\displaystyle \varphi _{1}}
and
φ
2
{\displaystyle \varphi _{2}}
the standard parallels:
x
=
ρ
sin
θ
y
=
ρ
0
−
ρ
cos
θ
{\displaystyle {\begin{aligned}x&=\rho \sin \theta \\y&=\rho _{0}-\rho \cos \theta \end{aligned}}}
where
n
=
1
2
(
sin
φ
1
+
sin
φ
2
)
θ
=
n
(
λ
−
λ
0
)
C
=
cos
2
φ
1
+
2
n
sin
φ
1
ρ
=
R
n
C
−
2
n
sin
φ
ρ
0
=
R
n
C
−
2
n
sin
φ
0
{\displaystyle {\begin{aligned}n&={\tfrac {1}{2}}\left(\sin \varphi _{1}+\sin \varphi _{2}\right)\\\theta &=n\left(\lambda -\lambda _{0}\right)\\C&=\cos ^{2}\varphi _{1}+2n\sin \varphi _{1}\\\rho &={\tfrac {R}{n}}{\sqrt {C-2n\sin \varphi }}\\\rho _{0}&={\tfrac {R}{n}}{\sqrt {C-2n\sin \varphi _{0}}}\end{aligned}}}
= Lambert equal-area conic
=If just one of the two standard parallels of the Albers projection is placed on a pole, the result is the Lambert equal-area conic projection.
See also
List of map projections
References
External links
Mathworld's page on the Albers projection
Table of examples and properties of all common projections, from radicalcartography.net
An interactive Java Applet to study the metric deformations of the Albers Projection.