Ellipse Calculator
Area
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Approx Perimeter
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Eccentricity
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Foci Distance
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Ellipse Properties and Formulas
Area = pi*a*b. Perimeter uses Ramanujan approximation: pi(3(a+b) - sqrt((3a+b)(a+3b))), accurate within 0.01%.
Eccentricity e = sqrt(1 - b^2/a^2). Circle has e=0, elongated approaches 1. Planetary orbits are ellipses.
Foci: two points where sum of distances from any point on ellipse to both foci = 2a. Distance from center c = sqrt(a^2-b^2).
Frequently Asked Questions
Ellipse area?
A = pi*a*b. When a=b, it reduces to pi*r^2 (circle).
Exact perimeter formula?
No closed form exists. Ramanujan approximation is extremely accurate for practical use.
What is eccentricity?
Measures elongation. 0=circle, approaching 1=very elongated. Earth orbit: e~0.017.
What are foci?
Two special points inside. Sum of distances from any point on ellipse to both foci = 2a constant.