Quick Conversion on GIS Metrics
Basic parameter for the planet:

r
or Radius: 6371 km 
p
or Perimeter: 40,075 km
And the formula for arc length:
\[arc length=2\pi r\left ( \frac{\theta }{360} \right )=p\left ( \frac{\theta }{360} \right )\]\(\theta\)(central angle)  arc length  quick check 

1 arc degree  111.1 km  100 km 
0.5 arc degree (30 arc minutest)  55.7 km  50 km 
0.25 arc degree (15 arc minutest)  27.8 km  25 km 
0.1 arc degree (6 arc minutes)  11.1 km  10 km 
0.05 arc degree (3 arc minutes)  5.6 km  5 km 
0.01 arc degree (36 arc seconds)  1.1 km  1 km 
\(0.008\dot{3}\) arc degree (30 arc seconds)  928 m  900 m 
\(0.001\dot{6}\) arc degree (6 arc seconds)  186 m  200 m 
0.001 arc degree (3.6 arc seconds)  111 m  100 m 
坐地日行八万里。By毛泽东
The arc length i.e. perimeter of the Earth is about 40,000 km, which equals 80,000 Li (Chinese mile). Our planet rotates per day. According to elative motion, a people stays at the surface will have a 360 arc degrees motion. In some way, the people moves 40,000 km per day. Roughly, 1 arc degree equals 100 km at the surface of earth.
Arc Length Calculator
Reference:
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