How to determine the HTTP status without downloading the complete page?

curl -I fetches only the HTTP headers; it does not download the whole page. From man curl:

-I, --head
      (HTTP/FTP/FILE) Fetch the HTTP-header only! HTTP-servers feature
      the command HEAD which this uses to get nothing but  the  header
      of  a  document. When used on an FTP or FILE file, curl displays
      the file size and last modification time only.

Another option is to install lynx and use lynx -head -dump.

The HEAD request is specified by the HTTP 1.1 protocol (RFC 2616):

9.4 HEAD

   The HEAD method is identical to GET except that the server MUST NOT
   return a message-body in the response. The metainformation contained
   in the HTTP headers in response to a HEAD request SHOULD be identical
   to the information sent in response to a GET request. This method can
   be used for obtaining metainformation about the entity implied by the
   request without transferring the entity-body itself. This method is
   often used for testing hypertext links for validity, accessibility,
   and recent modification.

With wget, you need to use the --spider option to send a HEAD request like curl:

$ wget -S --spider https://google.com
Spider mode enabled. Check if remote file exists.
--2017-01-03 00:08:38--  https://google.com/
Resolving google.com (google.com)... 216.58.197.174
Connecting to google.com (google.com)|216.58.197.174|:443... connected.
HTTP request sent, awaiting response... 
  HTTP/1.1 302 Found
  Cache-Control: private
  Content-Type: text/html; charset=UTF-8
  Location: https://www.google.co.jp/?gfe_rd=cr&ei=...
  Content-Length: 262
  Date: Mon, 02 Jan 2017 15:08:38 GMT
  Alt-Svc: quic=":443"; ma=2592000; v="35,34"
Location: https://www.google.co.jp/?gfe_rd=cr&ei=... [following]
Spider mode enabled. Check if remote file exists.
--2017-01-03 00:08:38--  https://www.google.co.jp/?gfe_rd=cr&ei=...
Resolving www.google.co.jp (www.google.co.jp)... 210.139.253.109, 210.139.253.93, 210.139.253.123, ...
Connecting to www.google.co.jp (www.google.co.jp)|210.139.253.109|:443... connected.
HTTP request sent, awaiting response... 
  HTTP/1.1 200 OK
  Date: Mon, 02 Jan 2017 15:08:38 GMT
  Expires: -1
  Cache-Control: private, max-age=0
  Content-Type: text/html; charset=Shift_JIS
  P3P: CP="This is not a P3P policy! See https://www.google.com/support/accounts/answer/151657?hl=en for more info."
  Server: gws
  X-XSS-Protection: 1; mode=block
  X-Frame-Options: SAMEORIGIN
  Set-Cookie: NID=...; expires=Tue, 04-Jul-2017 15:08:38 GMT; path=/; domain=.google.co.jp; HttpOnly
  Alt-Svc: quic=":443"; ma=2592000; v="35,34"
  Transfer-Encoding: chunked
  Accept-Ranges: none
  Vary: Accept-Encoding
Length: unspecified [text/html]
Remote file exists and could contain further links,
but recursion is disabled -- not retrieving.