Автор: http://www.swissdelphicenter.ch

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;