# How do you find the arc length of a polar curve?

We can find the arc length $L$ of a polar curve $r = r \left(\theta\right)$ from $\theta = a$ to $\theta = b$ by
$L = {\int}_{a}^{b} \sqrt{{r}^{2} + {\left(\frac{\mathrm{dr}}{d \theta}\right)}^{2}} d \theta$