Inner Circular Arc Triangle Calculator

Calculations at a regular inner circular arc triangle. A regular inner circular arc triangle lies between three equal sized, touching circles. It is an equilateral triangle, which has circular segments with an angle of 60° removed from each side. The length of the triangle chord is equal to the radius.
Enter radius or arc length and choose the number of decimal places. Then click Calculate.

	Radius, chord (r, s):
	Arc length (a):
	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 an inner circular arc triangle.

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

Such a circular arc triangle is, in a sense, the counterpart to a Reuleaux triangle. The circular arc triangle lies between three tangent circles, three arcs are subtracted from an equilateral triangle here. The Reuleaux triangle is the intersection of three circles, three arcs are added to an equilateral triangle here. The arcs are defined by the side length of the equilateral triangle. Each of these two different shapes therefore consists of three identical arcs. The circular arc triangle and the Reuleaux triangle thus have the same perimeter if the underlying equilateral triangles have the same side length. This perimeter is larger than that of the corresponding equilateral triangle. The volume of the circular arc triangle is smaller than that of the equilateral triangle, by the same amount that the Reuleaux triangle's volume is larger.

The symmetry properties of the circular arc triangle are the same as those of the equilateral triangle and the Reuleaux triangle. It is axially symmetric about three axes, each passing through one vertex and the middle of the opposite side. Further, it is rotationally symmetric about the intersection of these three axes on a rotation of 120 degrees and multiples thereof. It is not point-symmetric.

Calculation of area and other dimensions: inner circular arc triangle

Last updated on 04/21/2026. Author: Jürgen Kummer

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