免费椭圆面积计算器
根据长轴和短轴计算椭圆的面积和周长近似值。
面积
75.3982
公式
## 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).
计算示例
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
常见问题
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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