Semi Minor Axis of Ellipse given Area and Eccentricity Calculator

Formula Used:

\[ b = \sqrt{\frac{A \cdot \sqrt{1 - e^2}}{\pi}} \]

Semi Minor Axis of Ellipse (b):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Semi Minor Axis of Ellipse?

The semi minor axis of an ellipse is half of the length of the shortest diameter of the ellipse. It is one of the two principal axes that define the elliptical shape, with the semi minor axis being the shorter of the two.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \sqrt{\frac{A \cdot \sqrt{1 - e^2}}{\pi}} \]

Where:

\( b \) — Semi minor axis of ellipse (m)
\( A \) — Area of ellipse (m²)
\( e \) — Eccentricity of ellipse (unitless)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the semi minor axis of an ellipse given its area and eccentricity, using the mathematical relationship between these geometric properties.

3. Importance of Semi Minor Axis Calculation

Details: Calculating the semi minor axis is essential for understanding the complete geometry of an ellipse. It helps in various applications including orbital mechanics, architectural design, and engineering calculations where elliptical shapes are involved.

4. Using the Calculator

Tips: Enter the area of the ellipse in square meters and the eccentricity (a value between 0 and 1). The calculator will compute the semi minor axis length in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of eccentricity values for an ellipse?
A: The eccentricity of an ellipse ranges from 0 (a circle) to values approaching but not reaching 1 (highly elongated ellipse).

Q2: How does eccentricity affect the shape of an ellipse?
A: Higher eccentricity values indicate more elongated ellipses, while lower values indicate shapes closer to circular.

Q3: Can this calculator be used for circles?
A: Yes, when eccentricity is 0, the ellipse becomes a circle, and the formula simplifies accordingly.

Q4: What are practical applications of this calculation?
A: This calculation is used in astronomy for orbital paths, in optics for elliptical mirrors, and in various engineering applications involving elliptical geometries.

Q5: Are there limitations to this formula?
A: The formula assumes a perfect elliptical shape and may not account for real-world imperfections or three-dimensional variations.