Calculadora de Elipse
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
A = π·a·b ; P ≈ π(a+b)·[1 + 3h/(10+√(4−3h))] onde h = (a−b)²/(a+b)²
About this calculator
The Ellipse Calculator is a practical tool for determining the area and approximate perimeter of an ellipse based on the lengths of its semi-major axis (a) and semi-minor axis (b). The ellipse is a common geometric shape in fields such as architecture, engineering, astronomy, and design. With this calculator, you get accurate results without having to deal with complex formulas manually.
The area calculation is straightforward: it uses the formula A = π·a·b, where π is approximately 3.14159. The perimeter of an ellipse, however, has no simple exact formula; therefore, we use Ramanujan's approximation, known for its high accuracy. The approximation is: P ≈ π(a+b)·[1 + 3h/(10+√(4−3h))], where h = (a−b)²/(a+b)². This formula is widely used because it yields very small errors for most ellipses.
You should use this calculator whenever you need the area or perimeter of an elliptical shape, such as in landscaping projects, calculating materials for oval windows, sizing ducts, or in analytic geometry problems. Simply enter the values of a and b (both must be positive and a ≥ b to avoid ambiguity) and click calculate.
Important precautions: ensure that the semi-axes are in the same unit. If a = b, the ellipse becomes a circle, and the perimeter formula reduces to 2πa. For very elongated ellipses (a much larger than b), Ramanujan's approximation is still good, but more complex formulas exist for extreme precision. This calculator is suitable for most practical applications.
Frequently asked questions
What are the semi-major and semi-minor axes of an ellipse?
The semi-major axis (a) is half the length of the longest axis of the ellipse, and the semi-minor axis (b) is half the length of the shortest axis. Both are measured from the center of the ellipse.
Is Ramanujan's approximation for the perimeter accurate?
Yes, Ramanujan's approximation is very accurate for most ellipses, with an error typically less than 0.04%. For very eccentric ellipses, the error may be slightly larger but still acceptable for practical purposes.
Can I use negative values for the semi-axes?
No, the semi-axes must be positive numbers. Negative values are not geometrically meaningful as they represent lengths.
What happens if a is less than b?
The calculator assumes a is the semi-major axis and b is the semi-minor. If you swap them, the area result will be the same, but the perimeter may differ slightly. It is recommended to input a ≥ b for consistency.
What are the units of the results?
The results will have the same units as the semi-axes you entered. For example, if you input in meters, the area will be in square meters and the perimeter in meters.