Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Measuring the circumference of an ellipse
Name: existing
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995

Is there any way to evaluate the circumference of an ellipse (when it is not a circle) exactly?

Approximately: 2 * pi * sqrt[(a^2 + b^2)/2] Exactly: 4 * a * E where E is an elliptic integral with k = sqrt[a^2 - b^2]/a


Revised April, 2001
I remember one from Ramanujan, and suggest the following addendum... see:

for the following approximation due to Ramanujan:

C ~~ (3a + 3b - sqrt[(a+3b)(b+3a)])

additionally, about _vinculum_ I seem to remember the more usual word for chain in Latin is _catena_ from which we get "catenary" (the hanging chain curve) and "concatenate" (joining with a chain, or joining the links of the chain together).... Gratiae!!! (thanx) for the Latin lesson in a most unexpected place!

Bob "A"

Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory