Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Circumference of an Ellipse

Date: 5/18/96 at 15:54:16
From: Anonymous
Subject: Circumference of an ellipse

Is there a formula for determining the circumference or distance 
around an ellipse?  I have looked in several geometry books, and 
searched newsgroup archives.  

Thanks.   Chan Peas

Date: 6/5/96 at 17:7:16
From: Doctor Ceeks
Subject: Re: Circumference of an ellipse

Determining the circumference of an ellipse to any degree of accuracy 
is a well understood problem.  In principle, computation of the arc 
length of any explicitly given curve to any degree of accuracy has 
been understood since the time of Newton (maybe Archimedes knew too!).  
The ideas of integral Calculus are applicable to the problem and give 
an algorithm for such a computation.

Note that the circumference of a circle can be computed to any degree 
of accuracy (in principle) because we know how to compute pi to any 
degree of accuracy (using, implicitly or explicitly, ideas of integral 

Assuming the value of pi, the circumference of a circle is 2*pi*r, 
where r is the radius.

An ellipse is specified by two parameters (major and minor axis) and 
there is no simple formula for the circumference of the ellipse in 
terms of these two parameters.

The area, however, is pi*a*b/4 where a and b are the lengths of the 
major and minor axes.

-Doctor Ceeks,  The Math Forum

Associated Topics:
High School Conic Sections/Circles
High School Geometry

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994-2015 The Math Forum