Racira Calculator

Ellipse Calculator

Ellipse Calculator

Area
47.1239
a = 5.00, b = 3.00 · perimeter ≈ 25.53
Perimeter
25.527
Eccentricity
0.800
Focal Distance
4.000
QuantityValue
Semi-major Axis (a)5.00
Semi-minor Axis (b)3.00
Area (πab)47.1239
Perimeter (Ramanujan)25.5270
Eccentricity (e)0.8000
Focal Distance (c = ae)4.0000
Flattening (f)0.4000
ShapeHighly elongated

Axes and Focal Distance

Summary Statistics
Area47.1239
Perimeter25.5270
Eccentricity0.8000
Focal Distance4.0000
Semi-major5.00
Semi-minor3.00

About the Ellipse Calculator

The area of an ellipse is the exact product πab — a circle is just the special case a = b. The perimeter has no elementary formula; the Ramanujan approximation used here, π(a+b)(1 + 3h/(10 + √(4 − 3h))), is accurate to within 0.04% for any shape.

Ellipses in the Real World

Planet orbits are ellipses with the Sun at one focus; whispering galleries focus sound at the two foci; and the Earth itself is an oblate ellipsoid with flattening ~1/298. Eccentricity quantifies each of these — from 0 (perfect circle) toward 1 (almost a line).

Frequently Asked Questions

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