Is there any formula for finding the ellipses perimeter in terms of the 2 axis?

Question

the formula should be such that of circle i.e P=2*3.14*R

if Some body knows just send ; else I have the Answer ; It is an Accadimic reaserch for proffesors in math or engineering to achive an accadimic degree if possible

I know that you can get the answer now using the computers or integral but what i need is simple formula used for any curved line.
thanks

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Answer 1

L (circumference) is approx. equal to:
pi * [ 1.5 * (a + b) - sqrt(a * b)]

a is the major radius
b is the minor radius

caveat: the static moments, both Cx and Cy must be 0.
C is the origin (i.e. the ellipse is centered about the origin)
.