Ellipse Calculator
Area, perimeter and foci 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.
- Area
- 87.9646
- Perimeter (approx.)
- 35.2032
- Eccentricity
- 0.82065
- Focus distance from centre
- 5.7446
- Foci at
- (±5.745, 0)
Quick answer
An ellipse has area πab; its perimeter has no simple closed form, so Ramanujan's approximation is used.
Area = πab
At a glance
| What it does | Area, perimeter and foci of an ellipse. |
|---|---|
| Category | Math |
| Inputs needed | Semi-major axis a, Semi-minor axis b |
| Main output | Area |
| Formula | Area = πab |
| Cost | Free — no sign-up, no download |
How to use the Ellipse Calculator
- 1Enter the semi-major axis (half the long diameter).
- 2Enter the semi-minor axis.
- 3Read area, perimeter and foci.
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 a7
- Semi-minor axis b4
Results
- Area87.9646
- Perimeter (approx.)35.2032
- Eccentricity0.82065
- Focus distance from centre5.7446
- Foci at(±5.745, 0)
Frequently asked questions
Why is the perimeter approximate?
The exact value needs an elliptic integral; Ramanujan's formula is accurate to a few parts per billion.
What is eccentricity?
How stretched the ellipse is: 0 is a circle, close to 1 is very elongated.
What do I need to enter into the Ellipse 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 Calculator work out the answer?
An ellipse has area πab; its perimeter has no simple closed form, so Ramanujan's approximation is used. It applies the formula Area = πab and shows the working so you can check each step by hand.
Is the Ellipse 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.