Albers projection



The Albers equal-area conic projection, or Albers projection (named after Heinrich C. Albers), 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.

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.

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 $${R}$$ is the radius, $$\lambda$$ is the longitude, $$\lambda_0$$ the reference longitude, $$\varphi$$ the latitude, $$\varphi_0$$ the reference latitude and $$\varphi_1$$ and $$\varphi_2$$ the standard parallels:


 * $$\begin{align} x &= \rho \sin\theta \\ y &= \rho_0 - \rho \cos\theta \end{align}$$

where
 * $$\begin{align} n &= \tfrac12 \left(\sin\varphi_1+\sin\varphi_2\right) \\

\theta &= n \left(\lambda - \lambda_0\right) \\ C &= \cos^2 \varphi_1 + 2 n \sin \varphi_1 \\ \rho &= \tfrac{R}{n}\sqrt{C - 2 n \sin \varphi} \\ \rho_0 &= \tfrac{R}{n}\sqrt{C - 2 n \sin \varphi_0} \end{align}$$

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.