Sinuosity or sinuosity index is a measure of deviation of a path between two points from the shortest possible path (the geodesic

Geodesic

In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...

, in planar geometries a straight line between the two points). It is given by the ratio of:

This sinuosity index is 1 in the case in which the actual path length is equal to the shortest path length, and can increase to infinity for a closed loop (where the shortest path length is zero) or for an infinitely-long actual path.

Rivers

In studies of rivers, the sinuosity index is similar but not identical to the general form given above, being given by:

The difference from the general form happens because the downvalley path is not perfectly straight. The sinuosity index can be explained, then, as the deviations from a path defined by the direction of maximum downslope. For this reason, bedrock streams that flow directly downslope have a sinuosity index of 1, and meander

Meander

A meander in general is a bend in a sinuous watercourse. A meander is formed when the moving water in a stream erodes the outer banks and widens its valley. A stream of any volume may assume a meandering course, alternately eroding sediments from the outside of a bend and depositing them on the...

ing streams have a sinuosity index that is greater than 1.