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Ellipse Circumference Approximation — result sheet
Estimate the circumference of an ellipse with the clearly labeled Ramanujan II approximation and its shape parameter.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: h=((a-b)/(a+b))^2; C ~= pi(a+b)[1+3h/(10+sqrt(4-3h))].
Ramanujan II estimates an ellipse circumference from two positive semiaxes without requiring numerical integration. The result is labeled approximate because a general ellipse circumference is not represented by an elementary exact formula and approximation error depends on shape.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Semiaxis a — length units; One positive ellipse semiaxis.; minimum 1.0E-6; maximum 1000000
- Semiaxis b — length units; The other positive ellipse semiaxis.; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Semiaxis a | 5 |
| Semiaxis b | 3 |
h=((5-3)/(5+3))^2=0.0625; Ramanujan II gives an approximate circumference of 25.52699886 length units.
Assumptions and limits
- a and b are positive semiaxes of one ideal axis-aligned ellipse and use the same length unit.
- The two semiaxes may be entered in either order; the shape parameter uses their squared relative difference.
- The returned circumference is a Ramanujan II estimate, not an exact perimeter, measurement uncertainty interval, or engineering tolerance.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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