Geometry
Aspect ratio and eccentricity
Eccentricity is zero for a circle and approaches one for a very long, thin ellipse.
The Formula
e = sqrt(1 - b^2 / a^2)
Eccentricity is zero for a circle and approaches one for a very long, thin ellipse.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| e | Eccentricity | none | How far from circular the ellipse is, between 0 and 1. |
| a | Semi-major axis | units | Half the longest distance across. |
| b | Semi-minor axis | units | Half the shortest distance across. |
What Each Symbol Means
enone
Eccentricity
How far from circular the ellipse is, between 0 and 1.
aunits
Semi-major axis
Half the longest distance across.
bunits
Semi-minor axis
Half the shortest distance across.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the area of an ellipse page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Area Of An Ellipse, filed under Math. Every number the guide produces comes from substituting into this one line.