Albers projection

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.

Country	Agency
Brazil	federal government, through IBGE, for Census Statistical Grid
Canada	government of British Columbia
Canada	government of the Yukon (sole governmental projection)
US	United States Geological Survey
US	United States Census Bureau

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}}(\sin \varphi _{1}+\sin \varphi _{2}),\\\theta &=n(\lambda -\lambda _{0}),\\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.

External links