Ellipse Area Calculator

The area equals pi times the semi major axis a times the semi minor axis b. When a and b are equal it reduces to pi times r squared, the area of a circle, which is why a = b = 4 gives 50.265482.

There is no simple exact formula for an ellipse perimeter, so this tool uses the Ramanujan second approximation: pi times (3(a+b) minus the square root of (3a+b)(a+3b)). It is accurate to many decimal places for the ellipses people usually work with.

Eccentricity measures how stretched the ellipse is. It is 0 for a perfect circle, sits between 0 and 1 for any ellipse, and climbs toward 1 as the shape becomes long and thin. At a = 8, b = 3 it is 0.927025, a clearly elongated oval.

It equals the square root of one minus the squared ratio of the shorter axis to the longer axis, using max(a, b) as the reference. Because it always divides the smaller by the larger, the result is the same no matter which field you label major.

It is the convention, and the labels assume it, but the math does not force it. Area and circumference are symmetric in a and b, and eccentricity uses the larger of the two internally, so swapping the values gives the same three answers.

A semi axis is half of a diameter. The semi major axis is half the longest width of the ellipse and the semi minor axis is half the shortest. If you measured the full widths, divide each by two before entering them here.

It is unit free, so pick any length unit and use it for both axes. Each field accepts values from just above 0 up to 1000 in steps of 0.1. Zero or negative axes are rejected because an ellipse needs two positive half axes.

Results are rounded to six decimal places and then displayed with up to six significant fraction digits, so a = 5, b = 3 reads 25.526986 rather than a shorter 25.53. You can round further yourself for a tidy final answer.

No. Every calculation runs locally in your browser as you type. Nothing is uploaded or saved, so the tool keeps working offline once the page has loaded.