Rose Calculator

Calculations at a rose or rosette. A rose is a curve, which in polar coordinates is formed by the equation r = a * cos( n * φ ). a is the radius of the circle surrounding the curve, which is also the length of one petal. For even n, the number of petals is twice n, for odd n it is equal. The more petals the rose has, the thinner is each single petal.
Enter the radius and the parameter n. Choose the number of decimal places, then click Calculate.

	Radius (a):			Rose with n=2 Rose with n=3
	Parameter (n):
	Number of petals (m):
	Area of one petal (B):
	Rose area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.
	Formulas: If n is even: $$m=2n$$ $$A=\frac{\pi a^2}{2}$$ $$B=\frac{A}{m}$$ If n is odd: $$m=n$$ $$A=\frac{\pi a^2}{4}$$ $$B=\frac{A}{m}$$ pi: $$\pi =\mathrm{3.141592653589793...}$$

The radius has a one-dimensional unit (e.g. meter), the areas have this unit squared (e.g. square meter). Parameter and unit are a dimensionless.

Roses are also defined for non-natural numbers, but then other shapes result which intersect themselves at points other than just the center. These can also include asymmetrical shapes. For rational numbers, the curves are closed, for irrational numbers they are open. Roses based on natural numbers are point-symmetrical to their origin and axially symmetrical to any straight line through the end of one of the petals and the center. Even-numbered roses have as additional axes of symmetry those straight lines that run exactly between two petals. The number of axes of symmetry is therefore n for odd-numbered roses, 2n for even-numbered roses, just like the number of petals. Even-numbered roses are rotationally symmetrical at an angle of 180 degrees divided by n, odd-numbered at an angle of 360 degrees divided by n.

A Foucault pendulum describes a rose curve. Roses are found as graphic decorative elements, although the rose as an ornament has a slightly different and more general meaning. Its name is derived from the flower rose, whose blossom is reminiscent of these shapes.

Last updated on 03/31/2026. Author: Jürgen Kummer

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