Segment of an Ellipse

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Ellipse segment (a two-dimensional figure) is an interior part of an ellipse bound by a chord and an ellipse.
• Chord is a line segment on the interior of the ellipse.
• Major axis is always the longest axis in an ellipse.
• Minor axis is always the shortest axis in an ellipse.
• Semi-major axis is half of the longest axis of an ellipse.
• Semi-minor axis is half of the shortest axis of an ellipse.

Segment Area formula

$$\large{ A_{area} = \frac{c\;d}{4} \; \left[ arccos \left( 1-\frac{2\;h}{c} \right) - \left( 1-\frac{2\;h}{c} \right) \; \sqrt{ \frac{4\;h}{c} } - \frac{4\;h^2}{c^2} \right] }$$
Symbol English Metric
$$\large{ A_{area} }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ c }$$ = major axis $$\large{ in }$$ $$\large{ mm }$$
$$\large{ d }$$ = minor axis $$\large{ in }$$ $$\large{ mm }$$