# How much a decimal degree is equal to in latitude 40N?

I would like to learn how much a decimal degree equals to 40N latitude as units of distance. I have this table (http://en.wikipedia.org/wiki/Decimal_degrees) in mind, but I am interested for the latitude 40N.

• Calculator by NGA and you can right-click the page and view the calculations via the document 'source.' – mkennedy Jan 29 '15 at 21:43
• At which bearing? Even along a single line of latitude, as the direction of travel changes, the decimal degrees required to travel some linear distance changes. The problem resolves to a partial differential equation, which is generally solved by numerical methods. – Vince Jan 29 '15 at 22:04 with

``````a (equatorial radius): 6,378,137.0 m exactly
e² (eccentricity squared): 0.006,694,379,990,14
``````

For an approximation the term `(1-e² sin² Φ)` is close to 0, so you get

`πa cosΦ / 180 = 111.319km cosΦ`

You can do another approach:

``````length of equator: U = 2πa = 2 * π * 6378137 m = 40075016 m
lenght of one degree: 40075 km/ 360 = 111.319 km
``````

All longitude have an equal lenght of 111319 m, for latitude you use simple trigonomety (considering the earth as a sphere) -> `111.319km cosΦ`

So, for 40° N it gives

``````111.319km cos 40° = 82.275 km
``````
• For a trivial question I don't have any problem to provide (or accept) a simple answer. The fist sentence of the Wikipedia already refer to latitude and longitude where you get more details. Apparently marika did not read even the first line of the article he posted himself. – Wernfried Domscheit Jan 30 '15 at 10:48
• I think the automatic criticism should also consider the length of the question! – Martin F Jan 30 '15 at 16:22
• Unfortunately the Wikipedia entry doesn't give the equations used to build the table, nor a link to another article that does (that I noticed). Hmmm, do I have the time to try to update it...? – mkennedy Jan 30 '15 at 17:32