Conic Family·Inventor: Heinrich C. Albers·Year: 1805

Albers Equal-Area Conic

"Equal-area conic projection standard for mid-latitude national thematic mapping"

Using two standard parallels where scale is exact, Albers Equal-Area Conic preserves true proportional surface area across large east-west landmasses like the contiguous United States, Europe, and China.

Forward Mathematical Formulation

X-COORDINATE:

x = \rho \sin[n(\lambda - \lambda_0)]

Y-COORDINATE:

y = \rho_0 - \rho \cos[n(\lambda - \lambda_0)]

DIFFERENTIAL METRIC:

\rho = \frac{\sqrt{C - 2n \sin \phi}}{n}, \quad n = \frac{1}{2}(\sin \phi_1 + \sin \phi_2)

Cartographic Application & Critique

Primary Applications: US Census Bureau national demographic maps, USGS National Atlas, Canadian and Australian national surveys.

Critical Analysis: Because census and resource data require rigorous area proportionality, Albers is the legal baseline for US governmental choropleth and demographic cartography.

TISSOT INDICATRIX (Lat: 60°N)Area: 1.02×

MERIDIAN (h)

1.13

PARALLEL (k)

0.90

ANGULAR (2θ')

13.2°

Tissot Profile Across Latitudes

LATITUDE	SCALE h	SCALE k	AREA hk	2θ' DEFORM
29.5°N	1.00	1.00	1.00×	0.0°
45.5°N	1.00	1.00	1.00×	0.0°
37.5°N	0.99	1.01	1.00×	1.4°
55°N	1.05	0.95	1.00×	6.2°

Interdisciplinary Geometric Links

ChromologiumSCALES

Choropleth Visual Density

JuralogiumPROVIDES

Congressional Districting Maps

Academic Provenance: Albers, H. C. (1805)