# Albers projection

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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.

## Contents

The Albers projection is used by the United States Geological Survey and the United States Census Bureau. [1] Most of the maps in the National Atlas of the United States use the Albers projection. [2] It is also one of the standard projections used by the government of British Columbia, [3] and the sole governmental projection for the Yukon. [4]

## Formulas

### For Sphere

Snyder [5] 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}}}

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## References

1. "Projection Reference". Bill Rankin. Archived from the original on 25 April 2009. Retrieved 2009-03-31.
2. Snyder, John P. (1987). Map Projections A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, D.C.: United States Government Printing Office. p. 2.
3. "Support & Info: Common Questions". Geomatics Yukon. Government of Yukon. Retrieved 15 October 2014.
4. Snyder, John P. (1987). "Chapter 14: ALBERS EQUAL-AREA CONIC PROJECTION". Map Projections A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, D.C.: United States Government Printing Office. p. 100.