# Perimeter of an Ellipse

The perimeter or circumference of an ellipse is difficult to determine accurately. Various approximation formulas are given for finding the perimeter of an ellipse.

**(a)** If the ellipse is very nearly in the shape of a circle (i.e., if the major and minor axes are nearly equal), then the perimeter is given by:

**(1)**

Where is the perimeter or circumference

is the semi-major axis

is the semi-minor axis

**(b)** When the ellipse differs from a circle (i.e., when there is a considerable difference between the major and minor axes), either of the followings may be used:

**(2)**

**(3)**

The result obtained by using formula (2) is too small and the result from formula (3) is too large. However, the mean or average of these results is approximately correct.

__Example__:

Find the perimeter of the ellipse whose major axis is cm, and whose minor axis is cm.

__Solution__:

** **Here ,

From (1): cm

From (2): cm

From (3): cm