Why i am unable to install OpenVPN in Windows 10?

Do VPNs use NAT?

If I'm running a public IP on my personal network, how does a VPN work?

I'm not sure if I even understand what the protocol is. For instance, this is some test code in C# to ping against a public ip address. Can anyone shed some light? In theory, someone else can run a program on their private IP which will have its port numbers changed by the VPN to be forwarded as if the packets actually came from the servers of the company where the private IP is running. The program will then be able to accept packets from the external server and deliver them to the client's LAN. The VPN works by masking out the original public ip and assigning you a new one with internal forwarding of all packets by the company.

You're correct - no need to get out your calculator. Just keep reading.

No, I was mistaken about the terminology of NAT, and your question made me realize it. NAT is an abbreviation for network address translation; it doesn't mean hiding a node behind a VPN-like interface. If anything, it makes your question more confusing, because NAT hides your private nodes behind another, typically public router. Your routers do that for you. So that's a whole different topic. You may know this but I'm clarifying it since some people are confused about that.

As we discussed before, it doesn't use NAT. It does use other protocols: OpenVPN encrypts packets and sends them down a tunnel through some other kind of system, such as a remote gateway or cloud provider. PPTP encapsulates/unwraps data and uses L2 communication over UDP to reach the destination. Cisco also talks L2 in PPTP. They might be encrypting L2 or L3 data too, but I couldn't tell you that. I don't own a Cisco router. I've just learned enough about it through a coworker who did.

There are a bunch of security issues with NAT. It exposes the outside world, sometimes accidentally, to the interior traffic of an enterprise network. So, it has security implications that some people don't always seem to understand. When this happens, it's a bad thing.