When to use this calculator
Estimate the circumference of an ellipse from its semi-axes. This is Ramanujan’s approximate perimeter, not an exact elliptic-integral evaluation.
Explore the circle & ellipse calculators for other questions in this topic. For a related calculation, use the Sector Area Calculator: Calculate a circular sector’s area from radius and angle in degrees.
PUTTING IT INTO PRACTICE
Ellipse Perimeter: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| First semi-axis | 5 |
| Second semi-axis | 5 |
| Result | 31.415927 units |
- Check the input labels and enter the example values above.
- Apply the relationship: Ramanujan approximation = π(a+b)(1+3h/(10+√(4−3h))); h=((a−b)/(a+b))².
- The result is 31.415927 units, rounded for display.
How to interpret your result
This is Ramanujan’s approximate perimeter, not an exact elliptic-integral evaluation.
Distinguish radius from diameter before entering measurements. Arc length follows the curve, while chord length runs straight between endpoints. Ring-shaped areas subtract the inner circle from the outer one.
Frequently asked questions
How is chord length different from arc length?
A chord is a straight line between two points on the circle. An arc follows the circular boundary between those points.
When is the ellipse perimeter calculator useful?
Estimate the circumference of an ellipse from its semi-axes. This is Ramanujan’s approximate perimeter, not an exact elliptic-integral evaluation.
How do I use the ellipse perimeter calculator?
Enter first semi-axis, second semi-axis. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Ramanujan approximation = π(a+b)(1+3h/(10+√(4−3h))); h=((a−b)/(a+b))².
What should I check before using the result?
This is Ramanujan’s approximate perimeter, not an exact elliptic-integral evaluation.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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