Ellipse Circumference
Calculate the circumference of an ellipse using Ramanujan first approximation formula. Free online ellipse circumference calculator with semi-major (a) and semi-minor (b) axis inputs for math and engineering.
About This Calculator
The Ellipse Circumference Calculator computes the perimeter of an ellipse using Ramanujan's first approximation formula. Unlike circles, ellipses do not have a simple closed-form expression for circumference -- the exact solution requires elliptic integrals.
Ramanujan's approximation provides accuracy within 0.04% for all ellipse shapes: C ≈ pi(a+b)(1 + 3h/(10 + sqrt(4-3h))) where h = ((a-b)/(a+b))^2. This is the most widely used approximation in geometry and engineering.
Frequently Asked Questions
What is the formula for ellipse circumference?
Unlike a circle, the ellipse has no simple exact formula for circumference. The Ramanujan approximation used is: C ≈ pi(a + b)(1 + 3h/(10 + sqrt(4 - 3h))) where h = ((a - b)/(a + b))^2, which is accurate to about 0.04% for all shapes.
Why is ellipse circumference hard to calculate?
Ellipse circumference requires elliptic integrals, which cannot be expressed with elementary functions. This is why approximations like Ramanujan's are used -- they provide excellent accuracy without requiring advanced calculus.
Is this calculator free?
Yes, all calculators on Calculy are completely free to use.