Behrmann Equal-Area Projection Calculator

It uses the defining standard parallels at 30 degrees north and south, accepts a configurable central meridian and sphere radius, and reports coordinates in the same unit as that radius. The calculation is deterministic, runs without a network connection, and preserves area on the spherical model. It is useful for checking formulas, preparing map coordinates, teaching projection behavior, and building repeatable geospatial workflows.

How the Behrmann projection transforms a coordinate

The Behrmann projection belongs to the cylindrical equal-area family. This calculator treats the Earth as a sphere and fixes the standard parallels at 30 degrees north and south, which is the defining choice for the Behrmann variant. Longitude controls the horizontal coordinate: the angular difference between the supplied longitude and central meridian is converted to radians, multiplied by the sphere radius, and scaled by the cosine of 30 degrees. Latitude controls the vertical coordinate through its sine, divided by that same cosine. Those paired scale factors make the transformation equal-area on the spherical model. The result is an x and y pair centered on the selected central meridian and equator. A point on the central meridian has x equal to zero, while a point on the equator has y equal to zero. The calculator also returns the fixed standard-parallel value, central meridian, and radius so each result carries the assumptions needed to interpret or reproduce it.

Choose inputs, units, and precision deliberately

Enter latitude and longitude in decimal degrees. Latitude must remain between -90 and 90, and longitude must remain between -180 and 180. The optional central meridian sets the longitude placed at the middle of the projected map; it defaults to zero degrees, the Greenwich meridian. Changing it shifts x coordinates but does not change y coordinates or the equal-area property. The radius defaults to 6,371,008.8 meters, a commonly used mean Earth radius. You may supply another positive radius for a different sphere or use a radius of one to obtain dimensionless coordinates scaled in sphere radii. Whatever unit you choose for the radius becomes the unit of x and y. The decimals option controls output rounding from zero through twelve places and defaults to six. Rounding happens only after the full projection calculation, reducing avoidable intermediate error. Inputs must be finite numbers; missing values, infinities, unsupported ranges, and nonpositive radii produce a typed invalid-input error rather than a misleading coordinate.

Understand appropriate uses and limitations

Use this capability when you specifically need the Behrmann spherical projection, want to compare cylindrical equal-area variants, or need a transparent coordinate calculation for a map workflow. Equal area means regions retain correct relative area on the sphere, which is valuable for thematic maps showing quantities such as population, habitat, land cover, or emissions. It does not mean shapes, distances, directions, or local angles remain correct everywhere. Distortion changes with latitude, and the polar regions are stretched horizontally in the familiar way of cylindrical equal-area maps. The calculation is not an ellipsoidal datum transformation and does not attach an EPSG coordinate reference system, false easting, false northing, or datum metadata. For surveying, navigation, cadastral work, or interchange with a GIS that requires an identified CRS, use a full geospatial library and a formally specified coordinate operation. For formula verification, education, reproducible visualization, and lightweight preprocessing on a spherical model, this calculator provides a focused and inspectable result.