Ellipse Perimeter Estimate
Ellipse Perimeter Estimate with explicit inputs, formulas and domain checks.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Ramanujan’s second approximation; not an exact elliptic-integral evaluation. Accuracy deteriorates for extremely thin ellipses. Inputs are semiaxes, not full diameters.
Example Calculation
- Semiaxis a: 5 units
- Semiaxis b: 3 units
Semiaxes5 and3 give a Ramanujan approximation of25.5270 units.
Frequently asked questions
How do I use this calculator?
Enter semiaxis a, semiaxis b. The result updates automatically. Use Reset to restore the example values.
What method does it use?
h=((a−b)/(a+b))²; P≈π(a+b)[1+3h/(10+√(4−3h))]. Ramanujan’s second approximation; not an exact elliptic-integral evaluation. Accuracy deteriorates for extremely thin ellipses. Inputs are semiaxes, not full diameters.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.