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I re-edit to simplify my question. My computer’s IP address is 192.168.1.10 and the router/gateway's IP is 192.168.1.1 (internal IP). I'm trying to find the external IP of my gateway or router. The router is connected to the ISP and id doesn't have a public IP, so that external IP should be a private IP. How can I find that external private IP?

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so www.ifconfig.me/ip isn't what you want? –  barlop Jun 3 '13 at 11:17
    
Try with traceroute (or hping in traceroute mode). With a bit of luck, you will see an answer from a private IP just before the connection enters the Internet, and that IP will be the one of the outside router. –  lserni Jun 3 '13 at 11:19
    
The router itself doesn't have the IP, A NI of the Router has an IP(and not a switches NI ports). On the LAN side of a home router, is a switch, just one IP 192.168.1.1 On the other side, if it's connected to your ISP it must be a WAN that end.. It's not designed for a LAN to be connected there. I haven't used more advanced routers though that allow LANs there, but if you're connected to your ISP, it's not designed to have a LAN there. It's meant to either connect straight to the wall(if the socket in your "home router" there is a telephone socket),(cont) –  barlop Jun 3 '13 at 12:35
    
or straight to a modem, if the socket is an ethernet/RJ45 socket labelled WAN. –  barlop Jun 3 '13 at 12:36
    
I think if it could connect a LAN on that side, then the Router's Administration IP(don't know what NI that'd be associated with), but that's show you the IPs of any port. On a regular home router, you have the switch ports which don't have IPs(the computers on them do). and the other side has an interface which gets an IP, but if it was a more professional router then that interface could be given an IP by the Router, and then, it'd show you what IP it is being given But also, even my home router tells me my internet ip address. If it was sent a private one(theoretically) it'd display that. –  barlop Jun 3 '13 at 12:40
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Try http://www.whatismyip.com/

This is what I always use when I need this info but cant access the modem.

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