Ellipse Calculator
Area exactly, perimeter by Ramanujan's approximation.
Area exactly, perimeter by Ramanujan's approximation. An ellipse's area is exactly πab — as clean as the circle it generalises.
Half the longest width.
Half the shortest width.
Area (units²)
47.1239
Perimeter ≈ 25.527 units
The area is exactly πab — as clean as the circle it generalises. The perimeter is not: it is an elliptic integral with no elementary closed form, so every ellipse perimeter formula in circulation is an approximation. This uses Ramanujan's second, accurate to better than one part in a hundred thousand here. Eccentricity 0.8 measures the departure from circular, where 0 is a circle and 1 is flat.
How the Ellipse Calculator works
An ellipse's area is exactly πab — as clean as the circle it generalises. Its perimeter is not: that is an elliptic integral with no elementary closed form, so every formula in circulation is an approximation. This uses Ramanujan's second, which is accurate to better than one part in a hundred thousand.
Also known as: area of an ellipse · ellipse perimeter calculator · ellipse circumference · oval area calculator
Where to go next
The Ellipse question rarely arrives on its own. These are the ones that usually come with it:
- Circle Calculator — Area, circumference, radius and diameter from any one of them.
- Surface Area Calculator — Six shapes, and the ratio that explains why small things cool fast.
- Circle Sector Calculator — Sector area, arc length and chord from a radius and an angle.
- Percentage Calculator — Every common percentage question in one place.
Frequently asked questions
How do I find the area of an ellipse?
Multiply π by both semi-axes. An ellipse 5 by 3 has an area of 15π, or 47.12 square units — exactly, with no approximation involved.
Why is the perimeter only approximate?
Because it has no closed form in elementary functions. The exact answer is an elliptic integral, and every 'ellipse perimeter formula' is an approximation of it. Ramanujan's second, used here, is among the best known.
What is eccentricity?
A measure of how far from circular the ellipse is, running from 0 for a circle to just under 1 for a nearly flat one. A 5 by 3 ellipse has an eccentricity of 0.8.
What are the foci?
The two points that define the ellipse: every point on the curve has the same total distance to both. For a circle they coincide at the centre.
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