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

Written by Jerry Ratzlaff on . Posted in Plane Geometry

The 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 formula

$$\large{ a = \frac{A}{\pi \;b} }$$

$$\large{ a = \frac {l} {1- \epsilon^2} }$$

$$\large{ b = \frac{A}{\pi \;a} }$$

$$\large{ b = a \sqrt {1- \epsilon^2} }$$

Where:

$$\large{ a }$$ = length semi-major axis

$$\large{ b }$$ = length semi-minor axis

$$\large{ A }$$ = area

$$\large{ \pi }$$ = Pi

$$\large{ l }$$ = semi-latus rectum

$$\large{ \epsilon }$$  (Greek symbol epsilon) = eccentricity