Circular Arc Quadrangle Calculator

Calculations at a straight circular arc quadrangle or quadrilateral. Such a circular arc quadrangle lies between four equal sized, touching circles. It is a square, which has a quarter circle removed from each side. The circular arc quadrangle resembles to an astroid, but is a different shape.
Enter one value and choose the number of decimal places. Then click Calculate.

	Circle radius (r):
	Lond diagonal (d):
	Short diagonal (e):
	Perimeter (p):
	Area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Construction of a circular arc quadrangle.

Radius, diagonals and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

A circular arc quadrangle lies between four identical circles, just as a circular arc triangle lies between three identical circles. However, there is an important difference. Aside from its size, such a circular arc triangle can only have one possible shape. This is because three identical circles that touch can only be aligned in one way. A circular arc quadrangle, on the other hand, does not have to be straight, like the one calculated here, but can also be distorted if the circles are shifted relative to each other. In that case, the underlying quadrangle is not a square, but a rhombus.
A right circular arc quadrangle is a special form of a right circular arc polygon that lies between any number of circles. With such a polygon, the number of possible distortions increases with the number of vertices.

The area of ​​such a circular arc quadrangle is that of a square minus that of a circle with a diameter equal to the side length of the square. If you inscribe a circle inside such a square and subtract its area, you get four pieces that can be joined together to form a circular arc quadrangle. For these pieces, see the missing pieces of the round corner. The perimeter of the circular arc quadrangle is the same as the circumference of this circle.

The symmetry properties of a right circular quadrangle are the same as those of a square. It is axially symmetric about four axes, two of which pass through opposite vertices and two through the midpoints of opposite sides. It is point-symmetric about the intersection of these four axes and rotationally symmetric about this point on a 90-degree rotation and multiples thereof.

Calculation of area and other dimensions: circular arc quadrangle

Last updated on 04/20/2026. Author: Jürgen Kummer

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