Circumference of an Ellipse

  • #1
is there a formula to find the circumference of an ellipse?
 

Answers and Replies

  • #2
jamesrc
Science Advisor
Gold Member
476
1
You can approximate it. An exact expression for the perimeter of an ellipse is
[itex] P = 4a\int_0^{\frac{\pi}{2}}\sqrt{1-e^2\sin^2{t}}dt [/itex]
where a is the semi-major axis, the eccentricity [itex] e = \frac{\sqrt{a^2-b^2}}{a} [/itex], and b is the semi-minor axis. This is found writing the equation of the ellipse in parametric form and using the arc-length formula. You can compute the integral numerically or write an approximation using a series expansion.

Here is a website with a number of approximations you can try out:

http://astronomy.swin.edu.au/~pbourke/geometry/ellipsecirc/ [Broken]
 
Last edited by a moderator:
  • #3
650
1
Length of the curve is given by


[tex] s=\int_a^b \sqrt{1+(\frac{dy}{dx})^2}dx[/tex]
where y=f(x) and x=a,x=b
 

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