Networks, and the internet, don't identify computers (of any size, even your smartphone) by the name you give them. Computers prefer numbers, and the numbers they use as identifiers are called IP addresses.
The "IP" stands for "internet protocol," which is part of the Transmission Control Protocol/internet Protocol (TPC/IP). It's all called IP for short, and TCP/IP is the language used for communication by most networks.
When it comes to your computer(s), there are actually several IP addresses involved. One is how the computer talks to the internet at large, which is the IP address of your router. That IP address is generally assigned to the router by your internet service provider (ISP); the router, in turn, handles all the traffic from your computers and other devices out to the internet. So even though a website only sees a request come in from the IP address on the router, the router knows how to route the information to/from the computer. (That's why it's called a router.)
Computers on internal networks, be it Wi-Fi or Ethernet, at home or in the office, have their own IP addresses assigned to them (usually by the router). That way, all the nodes on the internal network can communicate. The protocol used by the router to assign IP addresses is called Dynamic Host Control Protocol (DHCP).
If you have an IP address assigned, it's typically considered a "dynamic IP" because it could be temporary; the router might give the node in question a different IP address at a later time (same with the IP address your ISP gives your router). However, you can set up "static IP addresses" on computers so they never change—this can be important for some kinds of network communications, especially if it's crucial to be able to find that same node over and over. You could also get a static IP for your router—which is handy if you run a web server, for example, but expect your ISP to charge extra.
IP addresses are typically in the same format as a 32-bit number, shown as four decimal numbers each with a range of 0 to 255, separated by dots—each set of three numbers is called an octet. This format is used by IP version 4 (or IPv4). With it, you could—in theory—have 0.0.0.0 to 255.255.255.255 out there. However, this limited the world to a possible 4+ billion IP addresses, which isn't enough.
So, there's also IPv6, which is 128-bit, with eight groups of four hexadecimal digits (numbers and lower-case letters mixed), all separated by a colon (for example: 2001:0db8:85a3:0000:0000:8a2e:0370:7334). That offers a lot more than 4 billion addresses. The actual number is a 34 with 37 zeros after it (or 2 to the 128th power), which is technically 340,282,366,920,938,463,463,374,607,431,768,211,455. That's a lot of addresses.
That's all good to know, but how do you find your IP address?
Find Your Internet/Public IP Address
There may come a time when you need to know the IP address of your router, as assigned by your ISP. This can be particularly handy for things like VoIP calls or remote control software.
What you'll also find is that there's lots of information about you attached to that IP address, specifically your ISP's name and your general location (called a GeoIP). That's because ISPs dole out a range of IP addresses. Figuring out your provider and general location based on IP address is as simple as consulting a public list.
The simplest way to check your router's public IP address is to search "what is my IP?" on a search engine.
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With Google, that's all you see. There are plenty of sites out there that will show you the exact same thing. They see it simply because by visiting the site, your router has made a request, and thus revealed the IP address. Sites like WhatIsMyIP.com and IPLocation all go farther, showing off the names of your ISP, your city, and even maps.
The GeoIP info is far from foolproof. Generally, you're going to get an approximation of location—where the provider is, not the actual computer. In visiting those sites, I was told I was in Ithaca, New York...and Syracuse, New York. One gave a latitude/longitude that put me in North Carolina (which could be where my ISP has a data center, for all I know). Be sure to log out of your VPN service, too. Getting a real address for the public IP address usually requires a search warrant taken to the ISP.
Find Your Internal IP Address
Every device that connects to your internal network, be it at home or the office, has an IP address (your PC, your smartphone, your smart TV, your network printer, etc.) It doesn't matter if it's using Wi-Fi or Ethernet. They've all got an IP address if they're talking to the internet, or each other, through your router.
In the most basic network, your router is going to have an IP address like 192.168.0.1, and that will be called the "gateway." You'll see it pop up a lot as you look for the IP addresses of other devices. That typically means your router will use DHCP to assign addresses to devices, where only the last octet changes. So 192.168.0.101, or 192.168.0.102, for example. It depends on the range defined by your router.
This is pretty much the same on all internal networks, because they're hidden behind the router, which routes all that communication in and out to the proper places. If you have a big internal network, another number called a subnet will help divide your network into groups. The subnet mask used by most home networks is 255.255.255.0.
So how do you find it? In Windows there are a couple of methods. You can go to Start > Settings > Network & Internet. Under Wi-Fi click the wireless network you're on and look under Properties. If you're on an Ethernet connection, click Ethernet. You'll find all the data, plus buttons to copy it to paste in elsewhere.
The old-school method requires the command prompt. Search for "cmd" (without the quotes) using Windows search. Click to get the Command Line. In the resulting pop-up box, type "ipconfig" (no quote marks) then Return/Enter.
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What is revealed is more than just the IP address: you'll see the IPv4 address (and IPv6 if supported), the subnet mask, plus the Default Gateway (that's your router). Look above that row of data in the middle, and it shows the type of connection: "Wireless LAN adapter Wi-Fi." If I was using a wired connection it would have information under "Ethernet adapter."
On the Mac, go to the System Preferences, select Network, and it should be right there. Click the connection type on the left to see the IPs for each type. You may need to click the TCP/IP tab at the top with slightly older versions. Optionally, go full geek and open the Terminal and type "ipconfig" just like on Windows.
On an iOS/iPadOS, go into Settings > Wi-Fi, and click the "i" in a circle next to the network you're on. The IP address, subnet, and router (gateway) will all be there under both an IPv4 and IPv6 section, as seen below.
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If you need the IP address of other devices on your network, go into the router. How you access your router depends on the brand and the software it runs. In general, you should be able to type the router's gateway IP address into a web browser on the same network to access it. From there, you need to navigate to something like "attached devices." Then you get a full list of all the devices currently (or recently) attached to the network—and that list includes the IP address assigned to each device.
If you're lucky, you've got a modern router (or set of routers, like a mesh system) that can be controlled with mobile apps. The app may make it a lot easier to find the IP address(es) you want. Click the icon next to each device to show the IP address and more info for each.