Ellipse Perimeter Calculator (Ramanujan Approximation)
Enter the semi-major and semi-minor axis lengths of an ellipse to estimate its perimeter using Ramanujan's approximation.
Ellipse Perimeter Calculator (Ramanujan Approximation)
Estimate an ellipse's perimeter using Ramanujan's highly accurate approximation formula (there is no exact elementary formula for an ellipse's perimeter).
There's no simple exact formula for an ellipse's perimeter, so this calculator uses the Ramanujan approximation — one of the most accurate elementary approximations known — based on the ellipse's two semi-axes.
Example
- With the default values shown above, this calculator returns: h (used internally) ≈ 0.053254; Perimeter (Approximate) ≈ 41.39.
Frequently Asked Questions
Why is this an approximation?
Unlike a circle, an ellipse's exact perimeter requires an elliptic integral that can't be written with elementary functions. Ramanujan's formula used here is extremely accurate (typically within a tiny fraction of a percent) without needing that advanced math.
What if it's a circle?
When a = b, the formula correctly simplifies to the standard circle circumference, 2πr.