Home

Ellipse Definition and Equation Calculator

Online ellipse calculator: enter the semi-major and semi-minor axes a, b (a>b) to get the focal distance, foci and eccentricity.

展开更多 ▾
x²/a²+y²/b²=1, c²=a²−b²
F₁F₂a
a>b>0
Semi-minor

📖 Tutorial | Ellipse

1. Definition
Points whose sum of distances to F₁, F₂ is the constant 2a form an ellipse, equation x²/a²+y²/b²=1 (a>b>0).
2. Formula & Notation
a,bSemi-axes
cc²=a²−b²
3. Properties & Laws
  • Foci (±c,0);
  • c²=a²−b²;
  • 0<e<1, smaller is rounder;
  • Major axis 2a.
4. Steps
  1. Enter a>b>0;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: 5,4: c=3, foci (±3,0), e=0.6.
6. Common Pitfalls
Minus sign in c²;
Need a>b;
e<1.

❓ FAQ | Ellipse

Definition?
Sum 2a.
c?
a²−b².
Foci?
(±c,0).
e?
c/a<1.
Round?
Small e.
a=b?
A circle.
Foci on y?
y² first.