Calculate the area, approximate perimeter, eccentricity, and focal distance of an ellipse from its semi-axes.
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47.12
Area
25.53
Perimeter (approx.)
0.8
Eccentricity
4
Focal distance
5 / 3
Semi-major / Semi-minor
Also in General
Geometry
Calculate the area, approximate perimeter, eccentricity, and focal distance of an ellipse from its two semi-axis lengths.
Area = pi * a * b, where a and b are the semi-major and semi-minor axes. Unlike the circle, the exact perimeter of an ellipse has no simple closed-form expression.
The Ramanujan approximation gives a highly accurate estimate: P ≈ pi * (3(a+b) - sqrt((3a+b)(a+3b))). Eccentricity measures how "stretched" the ellipse is: e = sqrt(1 - (b/a)^2), where 0 is a circle and values approaching 1 are very elongated.
A = pi * a * b
Exact area.
e = sqrt(1 - (b/a)^2)
Eccentricity, 0 ≤ e < 1.
The perimeter uses the Ramanujan approximation, which is accurate to within 0.01% for most ellipses. The exact perimeter requires an elliptic integral.
Frequently asked questions
The ellipse becomes a circle. Area = pi * r^2, eccentricity = 0, and the perimeter equals the circumference 2 * pi * r.
The distance from the centre to each focus: c = sqrt(a^2 - b^2). An ellipse has two foci, equidistant from the centre along the major axis.
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