# What is the arclength between two points on a curve? How does it differ from the distance?

Nov 8, 2015

The distance is the arc length on a straight line. The arc length is the distance along the arc.

#### Explanation:

Example

For the points $\left(- 1 , 0\right)$ and $\left(1 , 0\right)$,

the distance between the points (the length of the straight line joining them) is $2$.

The length of the arc on the unit circle: ${x}^{2} + {y}^{2} = 1$ is half the circumference, so it is $\pi$. (More completely, the lengths of both the upper and lower arcs are $\pi$.)