Ellipse Calculator
Find an ellipse's area, circumference, eccentricity, foci, vertices and equation from its two semi-axes (and centre).
Change the values and press Calculate to work out your own figures.
Enter the two semi-axes and, optionally, the centre.
Show the working
- A = π a b
- e = c ÷ a, c = √(a² − b²)
- C = 4a E(e) (exact, by the arithmetic–geometric mean)
- Area = 47.1238898
How to use it
Enter the two semi-axes and, optionally, the centre.
Enter the measurements (decimals, fractions such as 3/4, or mixed numbers such as 1 1/2) and, if you like, their unit; the answer is then also given in other units. Show the working gives the formula.
Key facts
A = π a b; c = √(a² − b²); e = c ÷ a; (x − h)²/a² + (y − k)²/b² = 1
Eccentricity
e = 0 for a circle and approaches 1 as the ellipse flattens; Earth's orbit has e ≈ 0.017.
Questions
What is the area of an ellipse with semi-axes 5 and 3?
15π ≈ 47.1238898.
Where are the foci?
On the long axis, c = √(a² − b²) from the centre: 4 for a = 5, b = 3.
Formulas
A = π a b; c = √(a² − b²); e = c ÷ a; (x − h)²/a² + (y − k)²/b² = 1
Sources
Limitations
- All measurements in one calculation use the same unit; the answer is also given in other units.
- Measurements up to 10¹⁵.