uses
 Printers;
function GetPixelsPerInchX: Integer;
begin
 Result := GetDeviceCaps(Printer.Handle, LOGPIXELSX)
end;
function GetPixelsPerInchY: Integer;
begin
 Result := GetDeviceCaps(Printer.Handle, LOGPIXELSY)
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
 Caption := Format('x: %d y: %d DPI (dots per inch)',
  [GetPixelsPerInchX, GetPixelsPerInchY]);
end;