Area Of An Ellipse

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Calculate the area of an ellipse given its semi-major and semi-minor axes.

Ellipse Dimensions

Semi-major Axis (a)

Semi-minor Axis (b)

Calculation Results

301.59

Total Area (A)

The total surface space enclosed by the ellipse.

Perimeter (Approximate)63.46

Eccentricity (e)0.745

About this calculator

Understanding Ellipses

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the distances to the two focal points is constant. It is essentially a 'squashed' circle. The semi-major axis is half the longest diameter, and the semi-minor axis is half the shortest diameter.

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Pro Tips

If a = b, the ellipse is a circle.
The perimeter of an ellipse is much harder to calculate than its area, typically requiring complex approximations like Ramanujan's formula.
Eccentricity is a measure of how 'flat' the ellipse is, ranging from 0 (a circle) to almost 1.

Fun Facts

"The orbits of planets in our solar system are ellipses, with the Sun at one focus (Kepler's First Law)."
"Whispering galleries (like in St. Paul's Cathedral) are ellipsoidal; a sound made at one focus can be heard perfectly at the other."
"Lithotripters use ellipsoidal reflectors to focus shock waves to break up kidney stones without surgery!"

Formula: Area = π × a × b