Google Maps, like most web maps, works in WGS84, Web Mercator (Auxiliary Sphere) - EPSG 3857.
http://spatialreference.org/ref/sr-org/epsg3857-wgs84-web-mercator-auxiliary-sphere/
Planar units are meters.
Also, see this similar question.
PROJCS["WGS 84 / Pseudo-Mercator",
GEOGCS["WGS 84",
DATUM["WGS_1984",
SPHEROID["WGS 84",6378137,298.257223563,
AUTHORITY["EPSG","7030"]],
AUTHORITY["EPSG","6326"]],
PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
UNIT["degree",0.0174532925199433,
AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4326"]],
PROJECTION["Mercator_1SP"],
PARAMETER["central_meridian",0],
PARAMETER["scale_factor",1],
PARAMETER["false_easting",0],
PARAMETER["false_northing",0],
UNIT["metre",1,
AUTHORITY["EPSG","9001"]],
AXIS["X",EAST],
AXIS["Y",NORTH],
EXTENSION["PROJ4","+proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +wktext +no_defs"],
AUTHORITY["EPSG","3857"]]
The number comes from the tile resolution being set at a multiple of 256 pixels, and from the screen resolution (96dpi). Per Bing's page about their map tile system:
The map scale indicates the ratio between map distance and ground
distance, when measured in the same units. For instance, at a map
scale of 1 : 100,000, each inch on the map represents a ground
distance of 100,000 inches. Like the ground resolution, the map scale
varies with the level of detail and the latitude of measurement. It
can be calculated from the ground resolution as follows, given the
screen resolution in dots per inch, typically 96 dpi:
map scale = 1 : ground resolution * screen dpi / 0.0254 meters/inch
= 1 : (cos(latitude * pi/180) * 2 * pi * 6378137 * screen dpi) / (256 * 2 level * 0.0254)
At the most zoomed in, that works out to ~591,658,711. That's slightly off from the 591,657,550.5 value for Google maps, but I think the error can be attributed to different decisions about how to do rounding.
Best Answer
The function signature is:
Given the documentation for the computeArea() function just above, I think you can safely assume it is in the same units as the radius, where "the default radius is Earth's radius of 6378137 meters".
Of course, the earth isn't as spherical as Google Maps might like it to be, so be careful about how you apply that distance...