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`r = (3*(a+b) - sqrt((3a+b)(a+3b)))/2`
Enter a value for all fields
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:
- (a) Ellipse Semi-major axis
- (b) Ellipse 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.
The Math / Science
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:
- r = radius of the circle
- a = semi-major axis of an ellipse
- b = semi-minor axis of an ellipse
Circle Calculators
- Circle Area - Computes the area of a circle given the radius (A = π r2).
- Area of Circle Arc Segment f(r,θ) - Computes the area of an arc segment of a circle given the radius (r) and angle (θ)
- Area of Circle Arc Segment Area f(r,h) - Computes the area of an arc segment of a circle given radius (r) and the depth (h) into the circle.
- Area of Circle Sector f(r,Θ) - Computes the area of a sector (pie slice) of a circle given the radius (r) and angle (Θ).
- Angle of Circle Sector f(r,h) - Computes the angle in a circle from the radius and depth of the chord.
- Area of Circle Annulus - Computes the area of an annulus (ring) given the inner radius (r) and outer radius (R).
- Radius of Circle from Center and a Point - Computes the radius of a circle given the center point (h,k) and any other point (x,y) on the circle.
- Circumference of Circle - Computes the circumference of a circle given the radius (C = 2 π r).
- Circle Arc Length - Computes the length of an arc length on a circle given the radius (r) and angle (Θ)
- Circle within a Triangle - Computes the radius of a circle inscribed within a triangle given the length of the three sides (a,b,c) of the triangle.
- Circle around a Triangle - Computes the radius of a circle that circumscribes a triangle given the length of the three sides (a,b,c) of the triangle.
- Circle Diameter from Area - Computes the radius and diameter of a circle from the area.
- Circle Radius from Circumference - Computes the radius of a circle given the circumference.
- Circle Circumference from Area - Computes the circumference of a circle given the area.
- Circle Radius from Area - Computes the radius of a circle given the area.
- Chord Length: Computes the length of a chord in a circle from the radius and height.
- Circle Radius from Chord - Computes the radius of a circle based on the length of a chord and the chord's center height.
- Equation of Circle from Center and Point Coordinates - Develops the general equation of a circle based on the coordinates of the center (h,k) and any point on the circle (x,y).
- Circle with same Perimeter as an Ellipse - Computes the radius of the circle with the same perimeter of an ellipse defined by the semi-major and semi-minor axes.
- Rectangles to Cover a Circle - Computes the number of rectangles needed to minimally cover a circle based on the circle's diameter and the length and width of the rectangles.