Given a latitude / longitude to a certain number of decimal places, how to tell the area covered (in metres)?

Question

If i have a position specified in latitude and longitude, then it can cover a box, depending on how many digits of accuracy are in the position.

For example, given a position of 55.0° N, 3.0° W (i.e. to 1 decimal place), and assuming a truncation (as opposed to rounding), this could cover anything that's 55.01° to 55.09°. This would cover the area in this box: http://www.openstreetmap.org/?minlat=55.0&maxlat=55.1&maxlon=-3.0&minlon=-3.1&box=yes

Is there anyway to calculate the area of that box? I only want to do this once, so a simple website that provides this calculation would suffice.

The main reason I want to do this is because I have a position to a very high number of decimal places, and I want to see how precise it is.

Answer 1

While the Earth isn't exactly spherical you can treat it as such for these calculations.

The North/South calculation is relatively simple as there are 180° from pole to pole and the distance is 20,014 km (Source) so one degree == 20014/180 = 111.19 km.

The East/West calculation is more difficult as it depends on the latitude. The Equatorial distance is 40,076 km (Source) so one degree = 40076/360 = 111.32 km. The circumference at the poles is (by definition) 0 km. So you can calculate the circumference at any latitude by trigonometry (circumference * sin(latitude)).