Sinuosity or sinuosity index or sinuosity coefficient of a continuously derivable curve having at least one inflection point, is the ratio of the curvilinear length (along the curve) and the distance (straight line) between the end points of the curve:
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.
The sinuosity of a sine function (over a whole number of half-periods) can be calculated to be 1.216.
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 meandering streams have a sinuosity index that is greater than 1.
Remarkable values 
With similar opposite arcs joints in the same plane, continuously differentiable:
- Leopold, Luna B., Wolman, M.G., and Miller, J.P., 1964, Fluvial Processes in Geomorphology, San Francisco, W.H. Freeman and Co., 522p.
- Mueller, Jerry (1968). "An Introduction to the Hydraulic and Topographic Sinuosity Indexes1". Annals of the Association of American Geographers 58 (2): 371. doi:10.1111/j.1467-8306.1968.tb00650.x.