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Ellipse Calculator


: [ 2×π×Sqrt((r1² + r2²)/2) ]

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Formula

Area of Ellipse = πr1r2
Volume of Ellipse = (4/3) πr1r2r3
Perimeter of Ellipse = 2πSqrt ((r1² + r2²) / 2)

where,
r1, r2 and r3 = radii

An Ellipse is a plane curve that results from the intersection of a cone by a plane that produces a closed curve. An ellipse is a locus of points in a plane such that the sum of the distances to two fixed points is a constant.

An ellipse is a curved line forming a closed loop, where the sum of the distances from two points (foci) to every point on the line is constant.  An ellipse is usually defined as the bounded case of a conic section.
Example:
Find the area and perimeter of an ellipse with the given radii 5, 10.

Step 1: Find the area.
Area = πr1r2 = 3.14 * 5 * 10 = 157.

Step 2: Find the perimeter.
Perimeter = 2πSqrt((r1² + r2²) / 2) = 2 * 3.14 * Sqrt ((5² + 10²) / 2)
= 6.28 * Sqrt((25 + 100) / 2) = 6.28 * Sqrt (125 / 2)
= 6.28 * Sqrt(62.5) = 6.28 * 7.90 = 49.612.

Find the volume of an ellipse with the given radii 5,6,10.
Step 3: Find the volume.
Volume = (4/3) πr1r2r3= (4/3) * 3.14 * 5 * 6 * 10 = 1.33 * 188.4 = 942