How far is a degree?

A degree is an angle, so how long is it on the ground? Take the meridian first. It runs from pole to pole, which is 180° of latitude and about 20 000 km, so

1° of latitude ≈ 111 km

(Earth is slightly squashed, so the exact value runs from about 110.6 km near the Equator to 111.7 km near the poles. For most work, 111 km is fine.) This is also the origin of the nautical mile: traditionally 1 minute of latitude, which gives 60 nautical miles per degree. One nautical mile is defined as exactly 1 852 m.

A degree of longitude is different. Meridians start 111 km apart at the Equator and then all squeeze into one point at each pole. A degree of longitude is the distance along a parallel, and parallels shrink with the cosine of the latitude φ:

1° of longitude ≈ 111.3 km × cos φ

That gives about 111 km at 0°, 96 km at 30°, 79 km at 45°, 56 km at 60° and only about 19 km at 80°. At 90° it is zero.