Suppose γ : [*a*, *b*] `->` **C** is a continuous function from an interval into the complex plane. This curve γ is called *rectifiable* if the following supremum is finite:

In an analogous manner (by replacing the absolute value with the Euclidean distance or a norm), one can define rectifiable curves γ : [*a*, *b*] `->` **R**^{n} and, more generally, γ : [*a*, *b*] `->` *V* where *V* is a metric space.

Every continuous and piecewise continuously differentiable curve γ : [*a*, *b*] `->` **C** is rectifiable, and its length can be computed as the ordinary Riemann integral