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Ellipse Perimeter Calculator

Approximate perimeter of an ellipse (Ramanujan).

Compute the perimeter of an ellipse from its semi-major (a) and semi-minor (b) axes using Ramanujan's second approximation, accurate to better than 10⁻⁵ for typical eccentricities.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

h = ((a − b) / (a + b))². P ≈ π(a + b)(1 + 3h / (10 + √(4 − 3h))).

In depth

Compute the perimeter of an ellipse from its semi-major (a) and semi-minor (b) axes using Ramanujan's second approximation, accurate to better than 10⁻⁵ for typical eccentricities.