Ellipse Area Calculator
Calculate the area of an ellipse using semi-major and semi-minor axes
Calculate Ellipse Area
Half of the longest diameter
Half of the shortest diameter
Choose measurement unit
Ellipse Properties
Area in Different Units
Formula Used
Area = π × a × b
Where a = 5.000 cm (semi-major axis), b = 3.000 cm (semi-minor axis)
Area = π × 5.000 × 3.000 = 47.1239 cm²
Example Calculation
Garden Ellipse Example
Problem: You want to plant an elliptical garden
Given: Semi-major axis = 8 meters, Semi-minor axis = 5 meters
Find: Area of the garden
Solution
Using the ellipse area formula: A = π × a × b
A = π × 8 × 5
A = π × 40
A = 125.66 square meters
This means you need about 126 m² of planting area.
Ellipse Diagram
Key Formulas
Area
A = π × a × b
Perimeter (approx.)
P ≈ π(a + b)
Ramanujan's approximation used
Eccentricity
e = √(1 - b²/a²)
Common Ellipse Examples
Tips & Facts
Semi-major axis (a) is always ≥ semi-minor axis (b)
When a = b, the ellipse becomes a circle
Eccentricity ranges from 0 (circle) to 1 (parabola)
Ellipses are conic sections formed by slicing a cone
Understanding Ellipses
What is an Ellipse?
An ellipse is an oval-shaped curve that looks like a squashed circle. It's defined as the set of all points where the sum of distances to two fixed points (called foci) is constant. Ellipses appear frequently in nature, from planetary orbits to the shape of shadows.
Key Components
- •Semi-major axis (a): Half of the longest diameter
- •Semi-minor axis (b): Half of the shortest diameter
- •Foci: Two fixed points that define the ellipse
- •Center: The midpoint between the foci
Area Formula Derivation
The area formula A = πab comes from calculus:
1. Start with the ellipse equation: x²/a² + y²/b² = 1
2. Solve for y: y = b√(1 - x²/a²)
3. Integrate from -a to a
4. Result: A = πab
Real-World Applications
- Astronomy: Planetary and satellite orbits
- Architecture: Arches and domes
- Engineering: Gears and cam profiles
- Art: Perspective drawing and design