How accurate is geolocation?

Is it possible to determine (or guess) how accurate is the location which a browser returns via the navigator.geolocation.getCurrentPosition() API?

If not with that API, any other API available (to a web server and/or to JavaScript running in a browser)?

Or more simply, is it possible to determine whether the location is (presumably accurately) returned from GPS, as opposed to an approximation/guess based on IP address or nearby WiFi networks?

Even if I did browser sniffing or something to determine whether the device model is designed with GPS hardware, but that wouldn't tell me whether the GPS is enabled and was used.