# An arc of 1 degree on earth's surface is equal to how many kilometers?

Sep 25, 2016

At the equator, ${1}^{o}$arc length = 111.32 km, nearly. At Baltimore ( $l a t i t u \mathrm{de} = {39.48}^{o} N$), this length is 111.16 km, nearly. At the poles, it is 110.95 km, nearly.

#### Explanation:

The equatorial radius of the Earth is 6378.1 km.

The difference is 21.3 km. The polar radius is 6366.8 km.

At latitude ${\theta}^{o}$ N/S, the radius is $6378.1 - \left(\frac{\theta}{90}\right) \left(21.3\right)$ km,

nearly.

An arc of 1 radian = the radial distance of the the latitude circle, from

the center.of the Earth.

${1}^{o} = \frac{\pi}{180}$ radian.

So, the arc length $= \left(\frac{\pi}{180}\right) \left(6378.1 - \left(\frac{\theta}{90}\right) \left(21.3\right)\right)$ km,

At the equator, $\theta = 0$ and this arc length = 111.32 km, nearly.

At Baltimore, $\theta = {39.48}^{o}$ and the length is 111.16 km, nearly.

At the poles, $\theta = {90}^{o}$ and the length = 110.95 km, nearly.

Note that this arc is along a great circle. If the arc arc is drawn by

traversing along a small circle, the length is less. If this small circle is

the latitude circle, apply a factor cos (latitude).