Ellipse Area Calculator
Calculate the area and approximate circumference of an ellipse from its semi-major and semi-minor axes.
Area
75.3982
Circumference31.7309
Eccentricity0.745356
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).
Example Calculation
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
Frequently Asked Questions
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