How to get extent from current resolution in OpenLayers 3 for printing

I need to print a map with a fixed scale of 1:500 horizontally on a A4 paper (297x210mm). The map is done with Openlayers, the print request is sent to QGIS server using WMS getPrint function.

Till now I used a variable scale, printing the map in the actual visible resolution:

var dpi = 120;
var a4_width = 297;
var a4_height = 210;
var inch = 25.4;

var width = Math.round(a4_width * dpi / inch);
var height = Math.round(a4_height * dpi / inch);


var extent = map.getView().calculateExtent([width, height]);

window.open("http://localhost/cgi-bin/qgis_mapserv.fcgi?SERVICE=WMS&VERSION=1.3.0&REQUEST=GetPrint&FORMAT=pdf&TRANSPARENT=true&LAYERS=all&CRS=EPSG:3857&map0:STYLES=&map0:extent="+extent+"&TEMPLATE=DIN_A4_horizontal (1:500)&DPI=120");

How can I calculate the extend of the printing area using the center part of the actual view?

Probably the solution is part of this answer, but I can't figure out how.