Elongated Quarter Circle Calculator

Calculations at an elongated quarter circle, a quarter circle with a matching rectangle attached that extends it directly downwards.
Enter the circle radius and the rectangle length. Choose the number of decimal places, then click Calculate. The length of the rectangle is the short straight side of the elongated quarter circle. The long side is this length plus the radius of the circle. The width of the rectangle is equal to the radius of the circle.

	Circle radius (r):
	Short straight side (a):
	Long side (b):
	Perimeter (p):
	Area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

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

Such an elongated quarter circle is essentially an elongated semicircle bisected lengthwise, or alternatively, a half stadium bisected widthwise. This shape can also be described as a rectangle with one rounded corner. The elongated quarter circle possesses three corners, each of which constitutes a right angle. It has three sides, two straight sides and a third side composed of two distinct parts, a circular arc and a straight line, joined without an intervening corner.
This shape appears relatively frequently in architecture and design. For instance, double doors in buildings, particularly the portal doors of churches and monumental structures, often feature this design. The passageway itself, the opening enclosed by these two doors, consequently takes the form of an elongated semicircle.

The extended quarter circle is a simple example of a two-dimensional chiral shape. Chirality means handedness. Thus, there are two variants of it, a left-handed one and a right-handed one, which are mirror images of each other and possess identical dimensions. This is immediately understandable by referring to the example of the portal doors mentioned above. A significantly more complex, three-dimensional chiral shape is, for instance, the snub dodecahedron.

Last updated on 04/27/2026. Author: Jürgen Kummer

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