Thesis: What is Curvature? Curvature is the value that is determined by the difference between a straight line and a curve. In the case of a surface, curvature is the measure of the difference of a curved plane to a plane. Another way to put curvature is the rate of change of direction of the curve.
Curvature
Curvature, in mathematics, the rate of change of direction of a curve with respect to distance along the curve. At every point on a circle, the curvature is the reciprocal of the radius; for other curves (and straight lines, which can be regarded as circles of infinite radius), the curvature is the reciprocal of the radius of the circle that most closely conforms to the curve at the given point.
Example:

Computations
Curvature is denoted with the variable, kappa (Îș).

One of the ways to find curvature would be finding the magnitude of the derivative of a unit tangent vector function with respect to arc length, given by the equation:


Short video with explanation and example:
https://www.youtube.com/watch?v=EMo0vaphXpU&ab_channel=TheMathSorcerer