Ellipse Area, Perimeter & Eccentricity Calculator

Geometry
Area, eccentricity and perimeter (Ramanujan-2) will be shown on Calculate.
If you enter b > a, calculator will auto-swap (and note it) because a is the semi-major axis (largest).
Note: Area is exact: A = π·a·b. Perimeter uses Ramanujan's 2nd formula (compact & highly accurate).

An Ellipse Area and Perimeter Calculator helps you quickly compute an ellipse’s area, perimeter, and key parameters using its major and minor axes. Understanding the geometry of an ellipse can be difficult, particularly when determining its area and perimeter. In contrast to circles or rectangles, an ellipse lacks a straightforward closed-form formula for its perimeter, which makes calculators quite beneficial.

What Is an Ellipse?

An ellipse is a smooth, closed curve that looks like a stretched circle. It has two axes:

  • Semi-major axis (a): the longest radius
  • Semi-minor axis (b): the shortest radius

You can think of an ellipse as the shape created when a circle is stretched along one direction.

Ellipse Eccentricity (e)

Eccentricity measures how “stretched” an ellipse is.

Its value lies between 0 and 1:

  • 0 → a perfect circle
  • Closer to 1 → more elongated ellipse

Formula:

e = 1 − b2 a2

Where:

  • a = semi-major axis
  • b = semi-minor axis

Area of an Ellipse

Formula:

A = π a b

Perimeter of an Ellipse

Formula:

Ramanujan’s Second Approximation (More Accurate)

P ≈ π (a+b) [ 1 + 3h 10 + 4 − 3h ]

Where:

h = (a−b) 2 (a+b) 2

How to Use Our Ellipse Area & Perimeter Calculator?

  1. Enter the “semi-major (a)” and “semi-minor (b)”.
  2. Ensure that ‘a’ shall be greater than ‘b’, else the values will be swapped.
  3. Click “Calculate” to find the area, perimeter, and eccentricity of an ellipse.

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