Ellipse Perimeter
Calculate the perimeter of an ellipse using Ramanujan approximation formula. Free online ellipse perimeter calculator accepts semi-major (a) and semi-minor (b) axes with precise estimation for all ellipse shapes.
About This Calculator
The Ellipse Perimeter Calculator estimates the distance around an ellipse using Ramanujan's approximation. While circles have a simple circumference formula (2pir), ellipses require approximation methods because the exact perimeter involves elliptic integrals not expressible in elementary functions.
This calculator uses Ramanujan's first approximation: C ≈ pi(a+b)(1 + 3h/(10 + sqrt(4-3h))) where h = ((a-b)/(a+b))^2, giving accuracy within 0.04% for all ellipse shapes. For a circle where a = b, this simplifies to exactly 2pia.
Frequently Asked Questions
What is the difference between ellipse circumference and perimeter?
For ellipses, circumference and perimeter refer to the same measurement -- the distance around the ellipse. Both terms are used interchangeably in geometry contexts.
How accurate is the Ramanujan approximation?
Ramanujan's first approximation is accurate to within 0.04% for all ellipses. For near-circular ellipses (a ≈ b), it is virtually exact. Even for very elongated ellipses, error stays under 0.1%.
Is this calculator free to use?
Yes, all calculators on Calculy are completely free to use.