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

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 formulas

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

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

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

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

Symbol 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 $$\large{ in }$$ $$\large{ mm }$$

Tags: Surveying Equations