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소개

Ellipse Calculator — Compute area, eccentricity, and foci of an ellipse. Enter Semi-major axis, Semi-minor axis to get an instant, accurate result.

공식

Area = π×a×b. Eccentricity = c/a where c = √(a²−b²). Perimeter is estimated with the Ramanujan approximation: π×(3(a+b) − √((3a+b)(a+3b))), where a and b are the semi-major and semi-minor axes.

단계별 안내

Enter the Semi-major axis.
Enter the Semi-minor axis.
Click Calculate to see your result instantly.

실제 예시

Example: With Semi-major axis = 5, Semi-minor axis = 3, the Ellipse Calculator gives Area: 47.1239, Eccentricity: 0.8, Foci Distance: 4.

자주 묻는 질문

Why is the perimeter only approximate?

There is no exact elementary formula for an ellipse's perimeter; the Ramanujan formula used here is a highly accurate approximation.

What does eccentricity tell you?

It measures how elongated the ellipse is — 0 is a perfect circle, and values closer to 1 are more stretched.

What inputs does the Ellipse Calculator need?

You'll need to provide: Semi-major axis, Semi-minor axis. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.

How accurate is the Ellipse Calculator?

The Ellipse Calculator applies the formula exactly as calculated — Area = π×a×b. Eccentricity = c/a where c = √(a²−b²). Perimeter is estimated with the Ramanujan approximation: π×(3(a+b) − √((3a+b)(a+3b))), where a and b are the semi-major and semi-minor axes. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.

Is the Ellipse Calculator free to use?

Yes, the Ellipse Calculator is completely free, requires no signup, and runs instantly in your browser.