Area of Elliptical Sector Calculator

Area of Elliptical Sector Formula:

\[ ASec = \frac{aSector \times bSector}{2} \times \left( \angle Sector - \atan\left( \frac{(bSector - aSector) \times \sin(2 \times \angle Leg(2))}{aSector + bSector + ((bSector - aSector) \times \cos(2 \times \angle Leg(2)))} \right) + \atan\left( \frac{(bSector - aSector) \times \sin(2 \times \angle Leg(1))}{aSector + bSector + ((bSector - aSector) \times \cos(2 \times \angle Leg(1)))} \right) \right) \]

Semi Major Axis of Elliptical Sector:

Semi Minor Axis of Elliptical Sector:

Angle of Elliptical Sector:

rad

First Leg Angle of Elliptical Sector:

rad

Second Leg Angle of Elliptical Sector:

rad

Area of Elliptical Sector:

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1. What is the Area of Elliptical Sector?

The Area of Elliptical Sector is the total quantity of plane enclosed by the boundary of the Elliptical Sector. It represents the region bounded by the elliptical arc and the two radii connecting the center to the endpoints of the arc.

2. How Does the Calculator Work?

The calculator uses the Area of Elliptical Sector formula:

Where:

\( aSector \) — Semi Major Axis of Elliptical Sector (m)
\( bSector \) — Semi Minor Axis of Elliptical Sector (m)
\( \angle Sector \) — Angle of Elliptical Sector (rad)
\( \angle Leg(1) \) — First Leg Angle of Elliptical Sector (rad)
\( \angle Leg(2) \) — Second Leg Angle of Elliptical Sector (rad)

Explanation: The formula calculates the area of an elliptical sector by considering the semi-major and semi-minor axes, the central angle, and the angles of the two legs connecting to the elliptical arc.

3. Importance of Area Calculation

Details: Calculating the area of an elliptical sector is important in various fields including astronomy, engineering, and architecture where elliptical shapes are commonly encountered. It helps in determining the surface area of elliptical components and in various mathematical computations involving ellipses.

4. Using the Calculator

Tips: Enter all values in the specified units (meters for axes, radians for angles). All values must be positive numbers. The calculator will compute the area of the elliptical sector in square meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between an elliptical sector and a circular sector?
A: An elliptical sector is bounded by an elliptical arc and two radii, while a circular sector is bounded by a circular arc and two radii. The calculation of area is more complex for elliptical sectors due to the elliptical shape.

Q2: Can I use degrees instead of radians?
A: The calculator requires angles in radians. To convert degrees to radians, multiply the degree value by π/180.

Q3: What are typical applications of elliptical sectors?
A: Elliptical sectors are used in orbital mechanics, architectural design, and in the design of various mechanical components with elliptical shapes.

Q4: Are there any limitations to this formula?
A: This formula provides an exact calculation for the area of an elliptical sector, but it requires precise input values and assumes a perfect elliptical shape.

Q5: How accurate is the calculator?
A: The calculator provides results with high precision (up to 6 decimal places) when accurate input values are provided.