About the Ellipse Calculator
An ellipse is a stretched circle: an oval whose shape is set by two measurements, the semi-major axis (half the longest width) and the semi-minor axis (half the shortest width). This calculator takes those two numbers, or the full width and height if you prefer, and gives the area, the circumference, the eccentricity that says how stretched it is, the distance from the centre to each focus and the latus rectum. The area has a simple formula, pi times a times b, but the perimeter has no exact closed form, so the calculator uses Ramanujan's approximation, which is accurate to a tiny fraction of a percent for everyday shapes.
Updated October 2026
How to use the Ellipse Calculator
- 1Choose whether you measured semi-axes or the full width and height.
- 2Enter the two lengths.
- 3Read the area and circumference.
- 4Check the eccentricity and the position of the foci.
- 5Use any unit; results follow the same unit.
Worked example
A running track's inner edge is modelled as an ellipse 120 metres long and 80 metres wide. The semi-axes are 60 and 40. The area is π × 60 × 40, about 7,540 square metres. The circumference is about 317.3 metres. The foci lie about 44.7 metres from the centre along the long axis, and the eccentricity is 0.745. The calculator performs these steps for any size.
Draw an ellipse in a garden using the string method. Push two stakes into the ground at the foci, loop a string around them and pull it tight with a third stake, then trace around keeping the string taut. The length of the loop equals twice the focal distance plus the long axis. The calculator gives the focal distance for your chosen semi-axes, so you can mark the stakes in the right places before you start.
Ellipses in the real world
- Planetary orbits are ellipses with the Sun at one focus.
- Whispering galleries use the reflecting property of the foci.
- Oval tables, mirrors and windows.
- Cross sections of cylinders cut at an angle.
- Camera lens apertures and fonts.
Tips
Measure the full width and height at the widest points, then switch to the full width option so you don't have to halve them yourself. If both axes are equal, the ellipse is a circle and the circumference becomes 2πr. For ovals that are egg-shaped rather than symmetrical, this calculator only gives an approximation.
Related tools
The Circle Calculator handles the round case, the Area Calculator covers other shapes, the Sphere Calculator and Cylinder Calculator go into three dimensions, and the Trigonometry Calculator helps with angles.
Features
- Semi-axes or full width and height
- Area and circumference
- Eccentricity and focal distance
- Latus rectum
- Ramanujan's accurate perimeter formula
- Works for circles too
Frequently asked questions
What is the formula for the area of an ellipse?
Pi times a times b, where a and b are the semi-axes. A garden bed 10 m long and 6 m wide has semi-axes of 5 and 3, so its area is π × 5 × 3, about 47.1 square metres.
How do I find the perimeter of an ellipse?
There is no simple exact formula. Ramanujan's approximation, π(a + b)(1 + 3h/(10 + √(4 − 3h))) with h = ((a − b)/(a + b))², is extremely accurate. For semi-axes 5 and 3 it gives 25.527.
What is eccentricity?
A number from 0 to 1 that measures how far the ellipse is from a circle. A circle has eccentricity 0. Higher values mean a flatter, more stretched shape. Eccentricity is the focal distance divided by the semi-major axis.
What are the foci?
Two special points on the long axis. The sum of the distances from any point on the ellipse to the two foci is constant, which is how you can draw an ellipse with a string and two pins.
Is an ellipse the same as an oval?
In everyday use, yes, though an oval can be any egg-like shape. A true ellipse is symmetrical and defined by the equation x²/a² + y²/b² = 1.
What is the latus rectum?
The chord through a focus that is perpendicular to the long axis. Its length is 2b² ÷ a, and it appears in the study of orbits and optics.