Ellipse Calculator
Calculate ellipse area, perimeter, eccentricity from semi-major and semi-minor axes
About this calculator
This ellipse calculator computes essential geometric properties of an ellipse including area, perimeter (circumference), and eccentricity using the semi-major and semi-minor axes as inputs. It's invaluable for students, engineers, architects, and scientists working with elliptical shapes in mathematics, physics, astronomy, or engineering applications. The tool eliminates complex manual calculations and provides instant, accurate results for ellipse analysis and design projects.
How to use
Enter the semi-major axis (longest radius) and semi-minor axis (shortest radius) values in the input fields. The calculator will automatically compute the ellipse's area using πab, perimeter using Ramanujan's approximation, and eccentricity using the standard formula. Results update instantly as you modify the input values.
Frequently asked questions
What's the difference between semi-major and semi-minor axes?
The semi-major axis is the longest radius from center to edge, while the semi-minor axis is the shortest radius perpendicular to it.
How accurate is the perimeter calculation?
The calculator uses Ramanujan's approximation formula, which provides highly accurate results for most practical ellipse perimeter calculations.
What does eccentricity tell me about an ellipse?
Eccentricity measures how stretched an ellipse is. Values near 0 indicate a circle, while values approaching 1 indicate a very elongated ellipse.