Ellipse Circumference Calculator

Enter the semi-major and semi-minor axes to calculate the circumference of an ellipse.

Semi-Major Axis (a):

Semi-Minor Axis (b):

Formula for Ellipse Circumference

This formula provides a highly accurate approximation of the ellipse circumference.

Result

Understanding Ellipse Circumference

An ellipse is a closed curve in a plane which resembles a flattened circle. It is defined as the locus of points such that the sum of the distances from two foci is constant. The circumference of an ellipse, also known as its perimeter, is the distance around the ellipse. Unlike a circle, there is no simple exact formula for the circumference of an ellipse in terms of elementary functions.

The formula used above is a highly accurate approximation developed by Ramanujan. It provides a practical way to calculate the circumference for various applications in mathematics, engineering, and design. The semi-major axis (a) is the longest radius of the ellipse, and the semi-minor axis (b) is the shortest radius.

This calculator is useful for students learning about geometry, engineers designing elliptical shapes, or anyone needing to calculate the perimeter of an ellipse for practical purposes. For further reading, you can explore resources on ellipse geometry and approximations for ellipse circumference.