This equation computes the equivalent radius of a circle whose circumference is the same as the ellipse specified by its major and minor axes.

In other words, input the major and minor axes of an ellipse and get our the radius of the circle that has the same circumference as the ellipse.

Practical Application

In practical application you might have a wood stove with an elliptical outlet port.  This occurs on some models of wood stoves, including the turn of the last century stoves dubbed Round Oak Stoves.  You can match your Round Oak Stove's elliptical outlet to a standard pipe by determining the radius of a round pipe you'd need to fit over the elliptical outlet.

An example model No 16 Round Oak stove had an elliptical outlet port that measured 8 inches long by 3 -  5/16 in wide (corresponding to semi-major axis of 4 inches and semi minor axis of 1.65625 inches).  When you enter the semi-major axis and semi-minor axis of the elliptical port of the Round Oak model No. 16 into this equation, you get a corresponding circle radius of 2.95 inches .  So, a 6 inch diameter round pipe should be able to snuggly fit over the outlet port of the stove if stretched to elliptical shape at one end.