The Circle with the Same Circumference of a Ellipse calculator estimates the radius of a circle whose circumference is the same as the ellipse specified by its major and minor axes.
INSTRUCTIONS: Choose units and enter the following:
Radius of Circle (r): The calculator returns the radius in meters. However this can be automatically converted to compatible units via the pull-down menu.
The formula for the circumference of a circle is:
The Rumanujan approximation for the circumference of an ellipse is:
`c = π[ 3(a+b) - sqrt((3a+b)(a+3b)) ]`
If we make them equal and solve for r, the formula for the radius of a circle with equal perimeter of an ellipse is:
`r = [ 3(a+b) - sqrt((3a+b)(a+3b))] / 2`
where: