Albers projection

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 ${\displaystyle R}$ is the radius, ${\displaystyle \lambda }$ is the longitude, ${\displaystyle {\lambda }_0}$ the reference longitude, ${\displaystyle \phi }$ the latitude, ${\displaystyle {\phi }_0}$ the reference latitude and ${\displaystyle {\phi }_1}$ and ${\displaystyle {\phi }_2}$ the standard parallels: $${\displaystyle \begin{array}{cc}x& =\rho \sin \theta ,\\ y& ={\rho }_0-\rho \cos \theta ,\end{array}}$$ where $${\displaystyle \begin{array}{cc}n& =\frac{1}{2}(\sin {\phi }_1+\sin {\phi }_2),\\ \theta & =n(\lambda -{\lambda }_0),\\ C& ={\cos }^2{\phi }_1+2n\sin {\phi }_1,\\ \rho & =\frac{R}{n}\sqrt{C-2n\sin \phi },\\ {\rho }_0& =\frac{R}{n}\sqrt{C-2n\sin {\phi }_0}.\end{array}}$$

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.