# 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.

The Albers projection is used by the United States Geological Survey and the United States Census Bureau. Most of the maps in the National Atlas of the United States use the Albers projection. It is also one of the standard projections used by the government of British Columbia, and the sole governmental projection for the Yukon.

## 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 ${R}$ 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{aligned}x&=\rho \sin \theta \\y&=\rho _{0}-\rho \cos \theta \end{aligned}} where

{\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}} 