Albers projection

Snyder[2] 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 ${\displaystyle {R}}$ is the radius, ${\displaystyle \lambda }$ is the longitude, ${\displaystyle \lambda _{0}}$ the reference longitude, ${\displaystyle \varphi }$ the latitude, ${\displaystyle \varphi _{0}}$ the reference latitude and ${\displaystyle \varphi _{1}}$ and ${\displaystyle \varphi _{2}}$ the standard parallels:

${\displaystyle {\begin{aligned}x&=\rho \sin \theta \\y&=\rho _{0}-\rho \cos \theta \end{aligned}}}$

where

${\displaystyle {\begin{aligned}n&={\tfrac {1}{2}}\left(\sin \varphi _{1}+\sin \varphi _{2}\right)\\\theta &=n\left(\lambda -\lambda _{0}\right)\\C&=\cos ^{2}\varphi _{1}+2n\sin \varphi _{1}\\\rho &={\tfrac {R}{n}}{\sqrt {C-2n\sin \varphi }}\\\rho _{0}&={\tfrac {R}{n}}{\sqrt {C-2n\sin \varphi _{0}}}\end{aligned}}}$

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.[5]