How to calculate "as the crow flies" maths?

Question

Looking through a used car sales site (Auto Trader UK), I noticed they use "as the crow flies" distances from your ZIP code.

Example (using shopping mall ZIP code)

According to Google Maps, driving distance between Wigan and Burton-upon-Trent is 77.9 miles by road, but 66 minutes "as the crow flies".

77.9/66.6 = 1.17

Is there a formula for finding the "as the crow flies" distance in miles when you know the driving distance, but not the "as the crow flies"?

Is it driving distance divided by 2, or am I wrong here?

Since StackExchange is about questions that can be answered, not discussed, I'd appreciate it if someone could point out the correct math here.

Answer 1

There is no relation between distance as the crow flies (which is the actual physical distance) and driving distance except as a lower bound. The driving distance can theoretically be any number that is at least as large as the distance as the crow flies. It could be that the only road that leads there first goes to China then takes a tour of Asia before coming back to your destination.

Answer 2

The "as the crow flies" distance is the geodesic distance on the sphere. The haversine formula gives the great-circle distance between two points on a sphere given their longitudes and latitudes.