Double Star Polygon Calculator

Calculations at a double star polygon, an eight-pointed star with rays of two different lengths. Long and short rays alternate. The base of this star is a regular octagon, on which edges isosceles triangles are attached.
Enter the base length as well as side length or height of each point. Choose the number of decimal places and click Calculate.

	Base length (b):
	Side length long ray (l1):
	Height long ray (h1):
	Side length short ray (l2):
	Height short ray (h2):
	Star diameter (d):
	Perimeter (p):
	Area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

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

Such eight-pointed stars featuring two different ray lengths are frequently used for decorative purposes. The wind rose, or compass rose, goes beyond mere decoration, although decorative appeal often plays a role when this is used. The long rays represent the four cardinal directions north, east, south, and west, while the four short rays represent the intercardinal directions northeast, southeast, southwest, and northwest. Wind roses with 16 points and three different ray lengths are also common, accommodating intermediate directions such as north-northeast. For even finer subdivisions, straight lines are simply drawn between the 16 rays.

This double star exhibits axial symmetry across eight lines. Four pass through pairs of opposite points, and four pass through pairs of opposite indentations. All axes of symmetry intersect at the star's center. The star possesses point symmetry with respect to this center, as well as rotational symmetry for rotations of 90 degrees and multiples thereof. Thus, its rotational symmetry is lower than that of a polygram with eight rays of equal length, though the other symmetries remain the same.

Stars with alternating rays of two different lengths can be created from regular polygons, provided the number of their vertices, thus the number of star points, is even. However, they only truly resemble a star when they have at least six points. It is also possible to create such a star with rays of varying lengths but uniform angles by using an isogonal polygon as the base shape.

Calculation of area and other dimensions: double star polygon

Last updated on 07/08/2026. Author: Jürgen Kummer

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