Conic Eccentricity Calculator
Classify any conic and find its eccentricity.
Enter your values
Choose one of: Ellipse, Hyperbola.
Enter the semi-major axis a you are working with.
Enter the semi-minor / conjugate axis b you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Classify any conic and find its eccentricity. |
|---|---|
| Category | Math |
| Inputs needed | Conic type, Semi-major axis a, Semi-minor / conjugate axis b |
| Main output | Eccentricity |
| Formula | e = c ÷ a, c = √(a² ∓ b²) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Conic type
- Choose one of: Ellipse, Hyperbola.
- Semi-major axis a
- Enter the semi-major axis a you are working with.
- Semi-minor / conjugate axis b
- Enter the semi-minor / conjugate axis b you are working with.
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.
What do I need to enter into the Conic Eccentricity Calculator?
Just 3 values: conic type, semi-major axis a, semi-minor / conjugate axis b. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Conic Eccentricity Calculator work out the 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. It applies the formula e = c ÷ a, c = √(a² ∓ b²) and shows the working so you can check each step by hand.
Is the Conic Eccentricity Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.