Ellipse area
Ellipse area A = πab: enter the two semi-axes to get the area plus a Ramanujan-approximated perimeter and the eccentricity; a semi-minor axis larger than the semi-major one is rejected, as is any non-positive value.
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Result
One quantity per line, ready to copy.
Enter a semi-major axis to calculate
What this tool does
- Compute the area of an elliptical table top, running track, mirror or flower bed, and get the perimeter for material length.
- Compare the eccentricity across different axis ratios to see how flat an ellipse is.
- Verify the formulas: area πab and eccentricity √(1 − b²/a²).
Example
Input
3
Output
半长轴 3 半短轴 2 的椭圆面积：18.849556 周长（拉马努金近似）：15.86544 离心率 e：0.745356 长度单位 u，面积 u²，体积 u³
For semi-axes 2 and 1 the area is 2π ≈ 6.283185 and the eccentricity √3/2 ≈ 0.866025; the Ramanujan perimeter gives 9.688448 (the exact value is about 9.688448).
Frequently asked questions
Is there an exact perimeter formula?
No elementary closed form exists — it needs elliptic integrals. This tool uses the Ramanujan approximation, accurate to about 1e-6, which is plenty for material estimates; use numerical integration for more.
What if the semi-minor axis is larger?
It reports an error. By definition the semi-minor axis cannot exceed the semi-major one, and the tool refuses to swap them silently so you never get a plausible-looking wrong number.
What happens when a = b?
It is a circle: area πa², eccentricity 0, perimeter 2πa. Use it as a cross-check against the circumference result.
Keywords：椭圆面积ellipse area椭圆周长离心率几何计算半长轴