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.

  1. 01Area = pi × 6 × 4 ≈ 75.3982
  2. 02Circumference ≈ pi × (30 - √(22 × 16)) ≈ 31.7302
  3. 03Eccentricity = √(1 - 16/36) ≈ 0.7454

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