Geometry
Equivalent circle radius
The radius of the circle with the same area as the ellipse.
The Formula
r = sqrt(a x b)
The radius of the circle with the same area as the ellipse.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| r | Equivalent radius | units | Radius of the area-matched circle. |
| a | Semi-major axis | units | Half the longest distance across. |
| b | Semi-minor axis | units | Half the shortest distance across. |
What Each Symbol Means
runits
Equivalent radius
Radius of the area-matched circle.
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.