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Squaring the Ellipse - Calculator

Name: Squaring the Ellipse - Calculator
Author: Jürgen Kummer

Calculator for the edge length of a square and the semi-axes of an ellipse, if both have the same area. The calculation of the ellipse circumference is very complicated, for this see the ellipse calculator. Please enter either the edge length of the square and one semi-axis of the ellipse, or the two semi-axes. The other values will be calculated.

	Square	Ellipse
Edge length:
First semi-axis:
Second semi-axis:
Area:

Round to decimal places.

The unit is the same for edge length and semi-axes. The area has this unit squared. For example, length in centimeters, area in square centimeters. The area A of an ellipse is calculated using this formula: A = π * a * b, where a and b are the lengths of the two semi-axes. The area of a square is, of course, its edge length to the power of two. Therefore the power of two is called squaring.

Example: square and ellipse with almost the same area. The semi-axes of the ellipse measure 90 and 63 pixels. The edge length of the square is 133 pixels.

An ellipse is a conic section. An elliptical surface is formed when the lateral surface of a cone is cut obliquely without touching the base. It has a center and two foci. In the case of a circle, which can be considered a special form of ellipse, these three points coincide. Ellipses possess the property of eccentricity, which can be determined numerically and is greater the more the two semi-axes differ.

Constructing an equally sized square from an ellipse using only a compass and straightedge, in other words squaring the ellipse, is generally impossible. There are no special cases where this would be feasible. This is because calculating the ellipse requires the mathematical constant pi (π), which is transcendental. This means that π cannot be expressed algebraically, so it cannot be calculated using basic arithmetic operations or roots. Therefore, such a length cannot be constructed.

Last updated on 01/22/2026. Author: Jürgen Kummer

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