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Eccentricity of an Ellipse Calculator

This calculator helps you determine the eccentricity (E) of an ellipse based on the values of its semi-major axis (a) and semi-minor axis (b). It’s useful in geometry, astronomy, and physics where ellipses describe orbits or shapes. Simply input the values, and the tool will compute how “elongated” the ellipse is.

Eccentricity of an Ellipse Calculator

Input Fields
If enabled, the result will update automatically when you change any value.

Eccentricity Calculation Formula

Formula
$$E = \frac{\sqrt{a^2 – b^2}}{a}$$

Where:

  • $$E$$ = eccentricity of the ellipse
  • $$a$$ = semi-major axis (must be greater than b)
  • $$b$$ = semi-minor axis

The eccentricity measures how much the ellipse deviates from being a circle. A value of 0 indicates a perfect circle, while values approaching 1 indicate a more elongated ellipse.

Eccentricity is a key property of ellipses, commonly used in orbital mechanics and conic section analysis. In astronomy, for example, planetary orbits are ellipses, and eccentricity determines how stretched these orbits are. To use this calculator, make sure the semi-major axis $$a$$ is larger than the semi-minor axis $$b$$. The result will always be between 0 and 1. This tool simplifies the math by using the classic formula and returning an instant result.

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