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.
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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.
Result
Area
47.12389
Perimeter
25.526999
Eccentricity
0.8
Focal distance
4
The perimeter uses the Ramanujan approximation. The length unit matches the input values and the area is in the squared unit.
How it works
- 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.
Frequently asked questions
- How is the area of an ellipse calculated?
- Using the semi-major axis a and semi-minor axis b, the area is π × a × b. Each of a and b is the distance from the center to the end of its axis.
- How does the ellipse area formula differ from a circle's?
- A circle uses a single radius r for πr², but an ellipse has two different radii, so its area is πab. When a equals b the ellipse becomes a circle, and both eccentricity and focal distance drop to 0.
- Is the perimeter exact?
- The perimeter of an ellipse cannot be expressed exactly with elementary functions, so this tool uses Ramanujan's second approximation. The error grows slightly as a and b differ more, but it stays accurate enough for practical use.
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