Ellipse Calculator

Calculate an ellipse’s area, circumference, foci distance, and eccentricity using the ellipse calculator below.

Solution:

Axis (a): 
Axis (b): 
Area (A): 
Circumference (C): 
Eccentricity (e): 
Foci Distance (c): 


An ellipse is a two-dimensional regular oval whose curve consists of points in which the sum of the distances from both foci are the same for any point in the curve.

diagram of an ellipse showing axis a, axis b, and foci distance c

While an ellipse is oval in shape, it is different from an oval in that it is mathematically defined, while any curve resembling a squashed circle is an oval.

How to Calculate the Area of an Ellipse

Area is the space occupied by a two-dimensional geometric shape. The area of an ellipse can be found using a simple formula.

Area Formula

The formula for ellipse area is:

A = πab

Thus, the area A is equal to pi times the semi-major axis a times the semi-minor axis b.

To find the area of a circle, use our circle area calculator.

How to Calculate the Circumference of an Ellipse

Circumference is the distance around a two-dimensional geometric shape, sometimes referred to as the perimeter.

Interestingly, the circumference of an ellipse cannot be exactly defined by simple mathematics, but several formulas can approximate it with varying degrees of accuracy.

Circumference Formula

A relatively simple and fairly precise formula to find the circumference fo an ellipse is:

C = π( 3(a + b) – (3a + b)(a + 3b) )

The circumference C is equal to pi times 3 times the semi-major axis a plus the semi-minor axis b, minus the square root of 3 times a plus b, times a plus 3 times b.

Try our circumference calculator to find the circumference of a circle.

How to Find the Foci Distance

An ellipse has two focus points, pluralized foci. The distance from the center-point of the ellipse to each focus is called the foci distance.

Foci Distance Formula

The formula to find the foci distance for an ellipse is:

c = a² – b²

The foci distance c is equal to the square root of a squared minus b squared.

How to Find the Eccentricity of an Ellipse

The eccentricity of an ellipse is the ratio of the foci distance to the semi-major axis length. The smaller the eccentricity, the closer the ellipse is to becoming a circle.

Eccentricity Formula

The formula to find ellipse eccentricity is:

e = ca

The eccentricity e is equal to the foci distance c divided by the semi-major axis length a.

You might also be interested in trying out circle calculator.