Ellipse Eccentricity Calculator
Eccentricity, foci and axes of an ellipse.
Enter your values
Enter the semi-major axis a you are working with.
Enter the semi-minor 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
- Foci
- (±4, 0)
- Major axis length
- 10
- Minor axis length
- 6
Quick answer
Eccentricity e = c/a where c = sqrt(a^2-b^2); e is between 0 (circle) and 1 (very flat ellipse).
c = sqrt(a^2-b^2), e = c/a
At a glance
| What it does | Eccentricity, foci and axes of an ellipse. |
|---|---|
| Category | Math |
| Inputs needed | Semi-major axis a, Semi-minor axis b |
| Main output | Eccentricity |
| Formula | c = sqrt(a^2-b^2), e = c/a |
| Cost | Free — no sign-up, no download |
How to use the Ellipse Eccentricity Calculator
- 1Enter the semi-major axis a (longer radius) and semi-minor axis b (shorter radius).
- 2Compute c = sqrt(a^2-b^2) for the focus distance.
- 3Divide c by a to get eccentricity.
Inputs explained
- Semi-major axis a
- Enter the semi-major axis a you are working with.
- Semi-minor axis b
- Enter the semi-minor axis b you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Semi-major axis a5
- Semi-minor axis b3
Results
- Eccentricity0.8
- Foci(±4, 0)
- Major axis length10
- Minor axis length6
Frequently asked questions
What does e close to 0 mean?
The ellipse is nearly circular.
What if a < b?
Swap them so a is always the larger semi-axis.
What do I need to enter into the Ellipse Eccentricity Calculator?
Just 2 values: semi-major axis a, semi-minor 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 Ellipse Eccentricity Calculator work out the answer?
Eccentricity e = c/a where c = sqrt(a^2-b^2); e is between 0 (circle) and 1 (very flat ellipse). It applies the formula c = sqrt(a^2-b^2), e = c/a and shows the working so you can check each step by hand.
Is the Ellipse 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.