Ellipse Area Calculator
Calculate the area and approximate circumference of an ellipse from its semi-major and semi-minor axes.
Surface
75.3982
Formule
## Ellipse Calculations ### Area **Area = pi × a × b** Where a is the semi-major axis and b is the semi-minor axis. ### Circumference (Ramanujan Approximation) **C ≈ pi × (3(a+b) - sqrt((3a+b)(a+3b)))** There is no exact closed-form formula for the circumference of an ellipse. Ramanujan's approximation is remarkably accurate. ### Eccentricity **e = sqrt(1 - b²/a²)** (when a ≥ b) Eccentricity ranges from 0 (circle) to 1 (degenerate line).
Exemple Résolu
Ellipse with semi-major axis 6 and semi-minor axis 4.
- 01Area = pi × 6 × 4 ≈ 75.3982
- 02Circumference ≈ pi × (30 - √(22 × 16)) ≈ 31.7302
- 03Eccentricity = √(1 - 16/36) ≈ 0.7454
Questions Fréquentes
What is an ellipse?
An ellipse is a stretched circle. It is the set of all points where the sum of distances to two fixed points (foci) is constant.
What is eccentricity?
Eccentricity measures how "stretched" the ellipse is. e = 0 is a perfect circle, and as e approaches 1, the ellipse becomes more elongated.
Why is the circumference formula approximate?
Unlike circles, there is no exact algebraic formula for the perimeter of an ellipse. It requires elliptic integrals. Ramanujan's formula is an excellent approximation.
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