Annulus Sector Calculator

Name: Annulus Sector - Geometry Calculator
Author: Jürgen Kummer

Calculations at an annulus sector, or circular ring sector. An annulus sector is a cut from an annulus, which is bordered by two straight lines from its center. Another way to define it is as a circular sector from which a smaller circular sector with the same angle and starting point is removed.
Enter the angle, as well as either both radiuses or one radius and the side length. Choose the number of decimal places, then click Calculate. Please enter angle in degrees, here you can convert angle units.

Formulas:

R = r + s

l = \frac{2 \cdot R \cdot π \cdot Θ}{360 °}

m = \frac{2 \cdot r \cdot π \cdot Θ}{360 °}

d = \sqrt{R^{2} + r^{2} - 2 R r \cdot \cos (Θ)}

p = l + m + 2 \cdot s

A = \frac{(R^{2} - r^{2}) \cdot π \cdot Θ}{360 °}

pi:

π = 3.141592653589793 ...

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

An annulus sector is a mathematically simple way to subdivide an annulus. Its area is calculated by taking the area of the annulus and multiplying it by the angle, then dividing by 360 degrees, or respectively 2π. The perimeter is calculated in a similar manner, whereas here the breadth of the annulus must be added twice to account for the straight sides. The perimeter of the annulus itself is hereby the sum of the outer and the inner circumferences.
Even simpler than a general annulus sector to calculate is a semi-annulus, a special case of the annulus sector with an angle of 180 degrees. The semi-annulus is also a special case of the annulus segment. However, calculating the general case of an annulus segment is significantly more complicated. Another way to subdivide the annulus sector is into an annulus stripe.
The annulus sector is axially symmetric about the angle bisector of the defining angle.

A circular sector is sometimes referred to as a pie slice. By analogy, the sector of an annulus might be called a two-dimensional donut slice. Geometrically, as a three-dimensional shape, this would be a torus sector whose cross-section is, in turn, an annulus sector.

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