NumberCals

Ellipse Area Calculator

Calculate area and approximate circumference of an ellipse from its semi-major and semi-minor axes.

About this calculator

The Ellipse Area Calculator on NumberCals is a free, mobile-friendly tool for anyone needing to calculate area and approximate circumference of an ellipse from its semi-major and semi-minor axes. Enter your values in the form below and the result is computed instantly — no sign-up, no installation, no waiting.

Formula used

A = π·a·b; C ≈ π·(3(a+b) − √((3a+b)(a+3b)))

What you'll need

  • Semi-major axis (a) (e.g. 5)
  • Semi-minor axis (b) (e.g. 3)

What you'll get

  • Area
  • Circumference (Ramanujan's approx.)
  • Eccentricity (e)
Formula
A = π·a·b; C ≈ π·(3(a+b) − √((3a+b)(a+3b)))

Frequently Asked Questions

Why is the circumference approximate? +

The exact circumference of an ellipse can only be expressed as a non-elementary elliptic integral. Ramanujan's second formula gives an excellent approximation (error < 0.04% for all valid ellipses).

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