Pointed Semicircle Calculator

Calculations at a here so called pointed semicircle. This shape is created by the gap between two touching circles, to which a semicircle is added with the flat side laying centrally above it. All of these parts have the same radius. The shape added to the semicircle is that of a half circular arc quadrangle. The circumference of the pointed semicircle is the same as that of one circle, the area is half of the enclosing square. A similar constructed shape ist that of a bulge.
Enter one value and choose the number of decimal places. Then click Calculate.

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

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

The height and width of this shape, that is the distance between the two equal vertices and the distance between the pointed vertex and the midpoint of the opposite arc, are equal. They measure twice the radius. Consequently, this shape fits into a square with exactly that side length. If the semicircle is separated from the other part, and that part is bisected through the point, the resulting two parts can be attached to the semicircle in such a way that the whole figure fills exactly half that square. Therefore, its area is equal to that of half the square. Its perimeter is equal to that of the circle with the same radius, as the shape consists of one semicircular arc and two quarter circular arcs.
This shape is axially symmetric about the line passing through the point and the midpoint of the opposite arc, it possesses no other symmetry. It has three vertices and no straight edges, but three curved edges, one convex and two concave. The pointed vertex has an angle of zero degrees, while the other two vertices are right angles. Thus, the sum of the angles is 180 degrees, just as in a triangle.

This shape is somewhat reminiscent of a face or a mask. Similar forms are used this way in design, with the two concave arcs representing or framing the eyes.

Calculation of area and other dimensions: pointed semicircle

Last updated on 07/25/2026. Author: Jürgen Kummer

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