You will need to call the Windows API function GetDiskFreeSpaceEx() and convert the returned integers to doubles, since integers greater than 2 gigabytes are not supported in Delphi. Example:

function GetDiskFreeSpaceEx(lpDirectoryName: PAnsiChar;
  var lpFreeBytesAvailableToCaller : Integer;
  var lpTotalNumberOfBytes: Integer;
  var lpTotalNumberOfFreeBytes: Integer) : bool;
  stdcall;
  external kernel32
  name 'GetDiskFreeSpaceExA';
procedure GetDiskSizeAvail(TheDrive : PChar;
                           var TotalBytes : double;
                           var TotalFree : double);
var
  AvailToCall : integer;
  TheSize : integer;
  FreeAvail : integer;
begin
  GetDiskFreeSpaceEx(TheDrive,
                     AvailToCall,
                     TheSize,
                     FreeAvail);
{$IFOPT Q+}
 {$DEFINE TURNOVERFLOWON}
 {$Q-}
{$ENDIF}
  if TheSize >= 0 then
    TotalBytes := TheSize else
  if TheSize = -  then begin
    TotalBytes := $7FFFFFFF;
    TotalBytes := TotalBytes * 2;
    TotalBytes := TotalBytes +  ;
  end else
  begin
    TotalBytes := $7FFFFFFF;
    TotalBytes := TotalBytes + abs($7FFFFFFF - TheSize);
  end;
  if AvailToCall >= 0 then
    TotalFree := AvailToCall else
  if AvailToCall = -  then begin
    TotalFree := $7FFFFFFF;
    TotalFree := TotalFree * 2;
    TotalFree := TotalFree +  ;
  end else
  begin
    TotalFree := $7FFFFFFF;
    TotalFree := TotalFree + abs($7FFFFFFF - AvailToCall);
  end;
end;
procedure TForm .Button Click(Sender: TObject);
var
  TotalBytes : double;
  TotalFree : double;
begin
  GetDiskSizeAvail('C:\',
                   TotalBytes,
                   TotalFree);
  ShowMessage(FloatToStr(TotalBytes));
  ShowMessage(FloatToStr(TotalFree));
end;