Ellipse Perimeter Calculator
Ellipse perimeter, sometimes called circumference, has no elementary exact formula for general axes. This tool uses Ramanujan’s accurate practical approximation.
How to use this calculator
- Enter the two semi-axis lengths, not full diameters.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by ellipse perimeter calculator
P ≈ π(a+b)[1 + 3h/(10 + √(4−3h))], where h = ((a−b)/(a+b))².
- P ≈ π(a+b)[1 + 3h/(10 + √(4−3h))], where h = ((a−b)/(a+b))².
- Use consistent units. This is an approximation, not a general exact elliptic-integral calculation.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
An ellipse has semi-major axis 8 and semi-minor axis 5.
Enter both positive semi-axis lengths; the Ramanujan approximation estimates the boundary length.
The result is an approximate ellipse perimeter in the same length unit as the axes.
Understanding the result
Ellipse perimeter, sometimes called circumference, has no elementary exact formula for general axes. This tool uses Ramanujan’s accurate practical approximation.
Use consistent units. This is an approximation, not a general exact elliptic-integral calculation.
Important notes
Use consistent units. This is an approximation, not a general exact elliptic-integral calculation.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
What if both axes are equal?
The ellipse becomes a circle and the result reduces to its circumference.
Do the axes need to be entered in order?
No. The formula is symmetric, although outputs label the larger value semi-major.
How should I interpret this result?
Use consistent units. This is an approximation, not a general exact elliptic-integral calculation.
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Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.