Tricorn Calculator

Calculations at a tricorn. A tricorn is formed by three semicircles of equal size, whose circle center is on one line. The centers of the two outer circles are opposite to each other on the edge of the inner circle. The emerging two lancet arches, of which base width and circle radius are equal, are removed from the central semicircle, the tricorn remains. The tricorn has height and width r.
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.

Construction of a tricorn.

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

Each of the three arcs of the tricorn has the same length. One of these three arcs is convex, two are concave. One arc has one-sixth the circumference of a circle. This shape therefore has half the circumference of a circle, but a smaller circumference than a semicircle, because the latter has an additional straight side. If the three corners of such a tricorn are connected, they form an equilateral triangle. The tricorn has a smaller area than this, because if you place an equilateral triangle and a matching tricorn on top of each other, the upper arc protrudes beyond and the other two protrude inside. But all three arcs bounded by the triangle are the same size, so more area is subtracted from the tricorn than added to it.
The tricorn has an axis of symmetry centrally through the convex arc and through the opposite long point. This shape has no other symmetries.

Tricorn hat is the name of a trident hat that emerged in the 17th century and sometimes had this shape. Today, the tricorn hat is still part of some traditional uniforms.

Last updated on 03/30/2026. Author: Jürgen Kummer

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