Squircle Calculator

A supercircle is created in the Cartesian coordinate system by the rule |x|ⁿ + |y|ⁿ = rⁿ. With n=2, it is a circle. With n=4, it is a squircle, a shape with the properties of a square and a circle. As n gets higher, the shape resembles more to a square. A supercircle is a special case of a superellipse or Lamé curve.
Enter one value and choose the number of decimal places. Then click Calculate. Radius and diameter refer to the distance of opposite straight lines.

	Radius (r):			Squircle x4 + y4 = r4
	Diameter (d):
	Perimeter (p):
	Area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14   decimal places.

The calculation of p is very complicated and uses the gamma function Γ and the Meijer G-function.
Radius, diameter and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

Superellipses were studied and described in the 19th century by the French mathematician Gabriel Lamé. Calculating them is complicated because the curve is defined by a power equation, and the integrals required for area and circumference cannot be expressed in terms of elementary functions. The gamma function is an extension of the factorial function to real and complex numbers. It is defined via integrals, which also appear in the context of this curve. Meijer's G-function represents a very general class of special functions used to describe many complicated integrals. It is defined by a contour integral in the complex plane and incorporates gamma functions in its definition. The lemniscate constant S is a value associated with the lemniscate of Bernoulli. It can be expressed using the gamma function, thereby providing another way to specify the area of ​​the supercircle.

The supercircle possesses square symmetry. It has four axes of symmetry that intersect at its center. It exhibits point symmetry with respect to this point and rotational symmetry under rotations of 90 degrees and multiples thereof. A supercircle is curved along its entire circumference, thus it contains no straight sections.

Calculation of area and other dimensions: squircle

Last updated on 06/10/2026. Author: Jürgen Kummer

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