# curvature

## Curvature and Radius of Curvature

**Curvature** (symbol, $\kappa$) is the mathematical expression of how much a curve actually curved. It is the measure of the average *change in direction* of the curve per *unit of arc*. Imagine a particle to move along the circle from point 1 to point 2, the higher the number of $\kappa$, the more quickly the particle changes in direction. This quick change in direction is apparent in smaller circles.