Conic Eccentricity Calculator
Classify any conic and find its eccentricity.
Enter your values
ⓘ Live results
Results
- Eccentricity
- 0.8
- Shape
- Ellipse
- Focal distance c
- 4
- Foci
- (±4, 0)
- Directrix
- x = ±6.25
- Latus rectum
- 3.6
- Area
- 47.1239
Quick answer
Eccentricity measures how far a conic departs from a circle: 0 is a circle, under 1 an ellipse, exactly 1 a parabola and above 1 a hyperbola.
e = c ÷ a, c = √(a² ∓ b²)
How to use the Conic Eccentricity Calculator
- 1Choose ellipse or hyperbola.
- 2Enter the semi-major axis a and the other axis b.
- 3Read the eccentricity, foci and directrix for graphing.
Worked example
Using the values the calculator loads with:
Inputs
- Conic typeEllipse
- Semi-major axis a5
- Semi-minor / conjugate axis b3
Results
- Eccentricity0.8
- ShapeEllipse
- Focal distance c4
- Foci(±4, 0)
- Directrixx = ±6.25
- Latus rectum3.6
- Area47.1239
Frequently asked questions
What is Earth's orbital eccentricity?
About 0.0167 — very nearly a circle, which is why the seasons come from axial tilt rather than distance.
Can eccentricity be negative?
No. It is a ratio of positive distances, so it starts at 0 and increases.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.