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Ellipse Area Formula:
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An ellipse is a closed curve on a plane that surrounds two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. It is a conic section formed by the intersection of a cone with a plane.
The calculator uses the ellipse area formula:
Where:
Explanation: The area of an ellipse is calculated by multiplying π by the semi-major axis (a) and the semi-minor axis (b).
Details: Calculating ellipse area is important in various fields including astronomy (planetary orbits), engineering (elliptical designs), architecture, and physics. It helps in determining the surface area of elliptical objects and structures.
Tips: Enter both semi-major axis (a) and semi-minor axis (b) values in the same units. Both values must be positive numbers greater than zero.
Q1: What's the difference between an ellipse and a circle?
A: A circle is a special case of an ellipse where both semi-axes are equal (a = b). In a circle, both focal points coincide at the center.
Q2: Can I use this calculator for oval shapes?
A: While ovals are often used colloquially to describe ellipses, technically an oval is any egg-shaped curve, while an ellipse has a specific mathematical definition. This calculator is designed for true ellipses.
Q3: What units should I use?
A: You can use any consistent units (meters, centimeters, inches, etc.). The area result will be in square units of whatever unit you used for the axes.
Q4: How accurate is the calculation?
A: The calculation is mathematically exact for perfect ellipses. The accuracy depends on the precision of your input values and the mathematical constant π.
Q5: What if my ellipse is rotated?
A: The area formula remains the same regardless of orientation. Rotation does not affect the area calculation, only the lengths of the semi-axes matter.