Circle with the Same Area as an Ellipse

The Circle with the Same Area of a Ellipse calculator computes the equivalent radius of a circle whose area is the same as the ellipse specified by its major and minor axes.

INSTRUCTIONS: Choose units and enter the following:

• (a) Semi-major axis
• (b) Semi-minor axis

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.

Related Equations

• Area of an Ellipse
• Circle with the Same Areas as an Ellipse
• Circle with the Same Perimeter as an Ellipse

The Math / Science

The formula for the circumference of a circle is:

        a = π• r²

The area of an ellipse is:

      a = π•a•b

Therefore, the formula for the radius of a circle with equal perimeter of an ellipse is:

    `r = sqrt(a*b)`

where:

• r = radius of the circle
• a = semi-major axis of an ellipse
• b = semi-minor axis of an ellipse.