I wanted to see what various sinuosity values actually looked like, so I wrote a small mma script using filtered random walks to visualize it. In the attached image a path is shown in each grid and in the top-left corner of each is the percent you have to add to the straight-line distance to get the path distance. eg: +20% is a 1.2 times multiplier, ie: add 20% of the straight-line length to get the path length

Sinuosity is the length of a path divided by the shortest distance between the endpoints. Its how much you have to multiply the straight-line distance between two points to get the real distance. Very useful for estimating distances