\begin{definition}[Definition:Curvature/Unit-Speed Parametric Form]
Let $C$ be a curve defined by a real function which is twice differentiable.
Let $C$ be embedded in a cartesian plane and defined by the parametric equations:
:$\begin{cases} x = \map x t \\ y = \map y t \end{cases}$
Suppose the curve has the unit-speed parametrization:
:$x'^2 + y'^2 = 1$
The '''curvature''' $\kappa$ of $C$ at a point $P = \tuple {x, y}$ is given by:
:$\kappa = \sqrt{x''^2 + y''^2}$
{{Help|Clearly this is unsigned curvature; the sign is somehow determined by the orientation of the plane and the curve}}
where:
:$x' = \dfrac {\d x} {\d t}$ is the derivative of $x$ {{WRT|Differentiation}} $t$ at $P$
:$y' = \dfrac {\d y} {\d t}$ is the derivative of $y$ {{WRT|Differentiation}} $t$ at $P$
:$x''$ and $y''$ are the second derivatives of $x$ and $y$ {{WRT|Differentiation}} $t$ at $P$.
\end{definition}