> [!summary] The arc length of a circle describes the distance covered on a circle > **Key Equation:** > Arc lengths: $s= r\theta$ >[!info]+ Read Time **⏱ 1 min** # Definition The Arc lengths of a circle are the distances covered between two points on a circle. The distance covered is like following the lines of the circle between two points. Often, we describe arc lengths in terms of $\theta$ rather than the two positions ## Derivation > [!warning] Assumptions In this derivation, assume the image below as a visual aid. ![[arlc_1.png|300]] $ \begin{array}{c} \text{To find the distance covered between two points on a circle} \\ \text{The total distance on a circle is the following where $2\pi =\theta$} \\ C = 2\pi r\quad (1)\\ \\ \text{Then the total distance to cover on a circle is some another of $2\pi r$:} \\ C = k 2\pi \quad (2) \\ \\ (1) = (2) \quad \\ 2\pi r = k 2\pi \\ r=k \\ \\ \text{So then the total distance covered can be stated as}\\ s=k\theta = r \theta \end{array} $ --- > 📚 Like this note? [Star the GitHub repo](https://github.com/rajeevphysics/Obsidian-MathMatter) to support the project and help others discover it! ---