Virtually all data fields this wiki talks about are on the native grid of COSMO-DE, a rotated latitude-longitude rectangular grid. Any precise measure of resolution must be expressed as both

• the (constant) angular distance of meridians from one grid point to its in
  this sense closest neighbor,
• the (constant) angular distance of parallels from one grid point to its in
  this sense closest neighbor.

As an approximation, this wiki uses the square root of the fraction of the area of the domain over the number of grid points in it. This area is another approximation: the surface area of a portion of a sphere’s surface. The portion is delimited by only the minimum and maximum of regular, i.e. non-rotated, latitude and longitude respectively. The sphere gets the radius 6370 km, Earth’s average radius.