Calculations at an elliptical sector. An elliptical sector is formed by an ellipse and an angle originating at its center. Enter both semi axes and two of the three angles Θ1, Θ2 and θ. Choose the number of decimal places. Then click Calculate. Please enter angles in degrees, here you can convert angle units. θ is the angle between both legs of the elliptical sector.
Formulas:
θ = Θ2 - Θ1
c = √ a² * b² / [ a² * sin²(Θ1) + b² * cos²(Θ1) ]
d = √ a² * b² / [ a² * sin²(Θ2) + b² * cos²(Θ2) ]
A = ab/2 * { θ - atan[ (b-a)sin(2Θ2) / (a+b+(b-a)cos(2Θ2)) ] + atan[ (b-a)sin(2Θ1) / (a+b+(b-a)cos(2Θ1)) ] }
The angles in the formula of the area have to be calculated as radian.
The lengths have a one-dimensional unit (e.g. meter), the area has this unit squared (e.g. square meter).
A sector is the area between two lines that both emanate from a specific point and intersect a segment of a geometric shape. For a circular sector, these lines are defined by two radii, whereas an ellipse has no radii. In this elliptical sector, the lines emanate from the center, just as in a circular sector. Another type of elliptical sector is the Kepler sector, in which the lines emanate from one of the focal points of the ellipse.
Another way to intersect a shape is with a segment, where only one line, a chord, divides it. This is the case, for example, with a straight elliptical segment where the chord is parallel to one of the semi-axes. The area of an oblique elliptical segment can be calculated from a corresponding elliptical sector by subtracting the area of the triangle with sides c and d and the angle θ between them.
The length of a part of an elliptical arc cannot be calculated algebraically. There is an approximation formula for the perimeter of a complete ellipse, but not for any arbitrary part of it. Therefore, the perimeter of this shape cannot be calculated here.
