Area of an Ellipse Calculator

A = π × a × b, where a and b are the semi-major and semi-minor axes.

Inputs

Result

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How to use this calculator

  • Enter the semi-major and semi-minor axes.
  • Read area; circumference is shown for reference.

About this calculator

An ellipse generalizes the circle: instead of one radius, two semi-axes (a and b). The area formula is just πab — a clean generalization. Circumference is harder; Ramanujan's second approximation gives high accuracy for any aspect ratio.

Frequently asked

What is "semi-major" vs "semi-minor"?+
"Semi" means half — these are half the long and short diameters of the ellipse.
Why no exact formula for circumference?+
Ellipse circumference involves an elliptic integral that has no closed form. The Ramanujan approximation is accurate to ~10⁻⁷ for any axis ratio.
When does an ellipse become a circle?+
When a = b. Then area = πa·a = πa² (the circle formula).
What is eccentricity?+
e = √(1 − b²/a²). It measures how "stretched" the ellipse is. e=0 is a circle; e→1 approaches a parabola-like shape.
How does this apply to orbits?+
Planetary orbits are ellipses with the sun at one focus. Earth's eccentricity is ~0.0167 (very nearly circular).

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