Ellipse Area Calculator
Calculate the area and approximate perimeter of an ellipse by entering the semi-major and semi-minor axes. Uses Ramanujan's approximation for perimeter.
How to Use the Ellipse Area Calculator
- Enter the required dimensions (length, width, radius, height, etc.).
- The area, volume, or other geometric value is computed instantly.
- Review the result along with the formula used.
- Adjust dimensions to compare different scenarios.
Quick Reference
| From | To |
|---|---|
| a=2, b=3 | 18.85 |
| a=3, b=5 | 47.12 |
| a=4, b=6 | 75.40 |
| a=5, b=8 | 125.66 |
| a=5, b=10 | 157.08 |
| a=10, b=15 | 471.24 |
Use Cases
- •Calculating dimensions for home improvement or DIY projects.
- •Solving geometry problems for school or professional exams.
- •Estimating material quantities needed for construction work.
- •Planning layouts and designs with precise measurements.
Formula
Formula: S = π × a × b. Perimeter ≈ π(3(a+b) − √((3a+b)(a+3b))) (Ramanujan approximation).
Frequently Asked Questions
How do you calculate the area of an ellipse?
Multiply π by the semi-major axis (a) and semi-minor axis (b): S = π × a × b.
How is the perimeter of an ellipse calculated?
There is no exact closed-form formula. Ramanujan's approximation P ≈ π(3(a+b) − √((3a+b)(a+3b))) is very accurate.
What are the semi-major and semi-minor axes?
The semi-major axis (a) is half the longest diameter, and the semi-minor axis (b) is half the shortest diameter of the ellipse.
Is a circle a special case of an ellipse?
Yes. When a = b = r, the ellipse becomes a circle with area πr² and perimeter 2πr.