Semi-major and Semi-minor Axis of an Ellipse

Written by Jerry Ratzlaff on . Posted in Plane Geometry

ellipse major minor 3The major axis is always the longest axis in an ellipse.

The minor axis is always the shortest axis in an ellipse.

 

Semi-major and Semi-minor Axis of an Ellipse formulas

\(\large{ a = \frac{A}{\pi \;b} }\)   
\(\large{ a = \frac {l} {1\;-\; \epsilon^2} }\)   
\(\large{ b = \frac{A}{\pi \;a} }\)   
\(\large{ b = a \sqrt {1 - \epsilon^2} }\)  

Where:

 Units English Metric
\(\large{ a }\) = length semi-major axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ b }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ \epsilon }\)  (Greek symbol epsilon) = eccentricity \(\large{ dimensionless }\)
\(\large{ \pi }\) = Pi \(\large{3.141 592 653 ...}\)
\(\large{ l }\) = semi-latus rectum \(\large{ in }\) \(\large{ mm }\)

 

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Tags: Surveying Equations