Perimeter of an ellipse How can I calculate the perimeter of an ellipse? What is the general method of finding out the perimeter of any closed curve?

I do not know if that's what you wanted, but the only general method is to calculate the length of the curve.
If we have a ellipse equation:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
with parametric representation:
$x=a \cos t, \ \ y=b \sin t, \ \ \ t\in [0,2\pi]$
the length of the curve is calculated knowing:
$x'=-a \sin t, \ \ y'=b \cos t, \ \ \ t\in [0,2\pi]$
and is (see Arc length)
$\int_{0}^{2 \pi} \sqrt{a^{2}\sin^{2}t+b^{2}\cos^{2} t} dt$
this integral can not be solved in closed form. There are various approximations (they take advantage of the power series) that you can see in this link
ellipse
