What is ellipse area?
A = πab.
Ellipse Calculator
Analyze an axis-aligned ellipse given semi-major and semi-minor lengths.
Enter a and b
Provide positive a and b (a is taken as the larger axis for eccentricity/foci).
About this calculator
How to use Ellipse Calculator, plus the formulas and logic behind the results.
Tool description
Ellipse area is πab. With A = max(a,b) and B = min(a,b), c = √(A²−B²) and eccentricity e = c/A.
How to use
- Enter positive semi-axes a and b.
- Select Calculate.
- Read area, c, eccentricity, and focus positions relative to center.
Formulas & reference
Area = π a bc = √(A² − B²) where A≥B are sorted axese = c/A
Ellipse facts
- 0 ≤ e < 1 for an ellipse
- Foci lie on the major axis
- Sum of distances to foci is 2A
- Area depends on both axes
Calculation logic
Uses M_PI for area. Sorts axes so eccentricity uses the major axis correctly whether a>b or b>a.
If a = b, the ellipse is a circle: c = 0 and e = 0.
Ellipse Calculator FAQ
Common questions about this calculator and how to use the results.
What is eccentricity?
e = c/A measuring how elongated the ellipse is.
Where are the foci?
At ±c from the center along the major axis.
What if a = b?
You have a circle with e = 0.
Must a be larger than b?
Not required—the calculator sorts them for c and e.
Is perimeter included?
Exact perimeter needs elliptic integrals; not computed here.