Area of Elliptical Segment Calculator

Area of Elliptical Segment Formula:

\[ A = \frac{2a \times 2b}{4} \times \left( \arccos\left(1 - \frac{2h}{2a}\right) - \left(1 - \frac{2h}{2a}\right) \times \sqrt{\frac{4h}{2a} - \frac{4h^2}{(2a)^2}} \right) \]

Major Axis of Elliptical Segment:

Minor Axis of Elliptical Segment:

Height of Elliptical Segment:

Area of Elliptical Segment:

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1. What is the Area of Elliptical Segment?

The Area of Elliptical Segment is the total quantity of plane enclosed by the boundary of the Elliptical Segment. An elliptical segment is a region of an ellipse cut off by a chord perpendicular to the major axis.

2. How Does the Calculator Work?

The calculator uses the Area of Elliptical Segment formula:

\[ A = \frac{2a \times 2b}{4} \times \left( \arccos\left(1 - \frac{2h}{2a}\right) - \left(1 - \frac{2h}{2a}\right) \times \sqrt{\frac{4h}{2a} - \frac{4h^2}{(2a)^2}} \right) \]

Where:

\( 2a \) — Major Axis of Elliptical Segment (m)
\( 2b \) — Minor Axis of Elliptical Segment (m)
\( h \) — Height of Elliptical Segment (m)
\( \arccos \) — Inverse cosine function
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the area of an elliptical segment by considering the geometric properties of the ellipse and the segment height.

3. Importance of Area Calculation

Details: Calculating the area of elliptical segments is important in various engineering, architectural, and mathematical applications where elliptical shapes are involved, such as in bridge design, architectural elements, and mechanical components.

4. Using the Calculator

Tips: Enter the major axis, minor axis, and height of the elliptical segment in meters. All values must be positive, and the height must be less than or equal to half the major axis.

5. Frequently Asked Questions (FAQ)

Q1: What is an elliptical segment?
A: An elliptical segment is the region of an ellipse that is cut off by a chord perpendicular to the major axis of the ellipse.

Q2: What are the units of measurement?
A: The calculator uses meters for all inputs, and the result is in square meters. You can convert from other units as needed.

Q3: What is the range of valid height values?
A: The height must be between 0 and half the major axis (0 ≤ h ≤ a). Values outside this range are not valid for an elliptical segment.

Q4: How accurate is the calculation?
A: The calculation uses precise mathematical functions and provides results with 6 decimal places accuracy.

Q5: Can this calculator be used for circular segments?
A: Yes, when the major and minor axes are equal (making it a circle), the formula simplifies to the standard circular segment area formula.