Ellipse Circumference Calculator
Estimate the circumference of an ellipse (Ramanujan approximation).
Input Data
Half of the long axis.
Half of the short axis.
Results
25.526986
Ellipse circumference ≈ 25.526986 (Ramanujan).
At a glance:The ellipse has no simple closed-form perimeter; the Ramanujan approximation is C ≈ π[3(a+b) − √((3a+b)(a+3b))].
Formula
C ≈ π[3(a+b) − √((3a+b)(a+3b))].
How to Use
- Enter semi-major axis a and semi-minor axis b.
- The tool returns the approximate circumference C.
Case Studies
a=5, b=3 → 25.527
C ≈ π[24 − √(18·14)] ≈ 25.527.
FAQ
Accurate?
The Ramanujan approximation error is tiny (<0.1%), fine for engineering.
Circle?
When a=b, C = 2πr.
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References
Content reviewed by the Calculatorism editorial team. Results are for reference only; please refer to the relevant authorities for the official figures.