Ellipse Area Calculator

Find the area of an ellipse from its semi major axis a and semi minor axis b, plus its perimeter, eccentricity and focal distance.

Input

Enter the semi major axis a and semi minor axis b of an ellipse to find its area (pi a b) along with its perimeter, eccentricity and focal distance.

Semi major axis a

Semi minor axis b

Area

47.12389

Perimeter

25.526999

Eccentricity

0.8

Focal distance

The perimeter uses the Ramanujan approximation. The length unit matches the input values and the area is in the squared unit.

The area of an ellipse is found from the semi major axis a and the semi minor axis b as area = pi times a times b. Here a and b are the distances from the center to the edge along each axis.
The perimeter cannot be expressed exactly with elementary functions, so this tool uses the second Ramanujan approximation. The error grows slightly as a and b differ more, but it stays accurate enough for practical use.
The eccentricity e measures how stretched the ellipse is, computed from the longer radius as e = square root of 1 minus shorter radius squared divided by longer radius squared. Values near 0 are nearly circular and values near 1 are very elongated.
The focal distance is the distance from the center to each focus, found from the longer radius as the square root of longer radius squared minus shorter radius squared. When a equals b the ellipse becomes a circle, and both the eccentricity and focal distance are 0.
The length unit matches the input values and the area is in the squared unit.

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