Ellipse Area Calculator
Calculate the area of an ellipse using the semi-major and semi-minor axes: A = π × a × b
Enter Semi-Major and Semi-Minor Axes
Step-by-Step Solution:
1. Formula: Area = π × a × b
2. Substitute: Area = π × 7 × 4
3. Multiply axes: 7 × 4 = 28
4. Multiply by π: 28π = 87.96 square units
Ellipse Area Formula
Area = π × a × b
where: - a = semi-major axis (half of the longest diameter) - b = semi-minor axis (half of the shortest diameter) - π ≈ 3.14159
How to Calculate Ellipse Area
- Identify the semi-major axis (a): Measure from the center to the farthest edge
- Identify the semi-minor axis (b): Measure from the center to the nearest edge
- Multiply the axes: Calculate a × b
- Multiply by π: Multiply the product by π (≈ 3.14159)
Understanding the Ellipse
An ellipse is a stretched circle. When both axes are equal (a = b), the ellipse becomes a circle. The formula πab generalizes the circle area formula πr², since for a circle, a = b = r.
The eccentricity of an ellipse measures how "stretched" it is: e = √(1 − b²/a²). A circle has eccentricity 0, while more elongated ellipses approach eccentricity 1.
Real-World Applications
Ellipse area calculations are used in: - Astronomy: Planetary orbits are elliptical (Kepler's first law) - Architecture: Elliptical arches and domes - Engineering: Elliptical cross-sections in pipes and ducts - Sports: Oval running tracks and stadiums - Optics: Elliptical mirrors and lenses
Common Questions
What is the formula for ellipse area?
The ellipse area formula is A = π × a × b, where a is the semi-major axis (half the longest diameter) and b is the semi-minor axis (half the shortest diameter).
What is the difference between an ellipse and a circle?
A circle is a special ellipse where both semi-axes are equal (a = b = r). The circle area formula πr² is a special case of the ellipse formula π × a × b when a = b.