Last updated: July 31, 2026
Ellipse Perimeter Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
h=((a-b)/(a+b))^2; perimeter ≈ π(a+b)(1 + 3h/(10 + √(4-3h)))
Where:
- a=a
- b=b
Worked Examples
a=8, b=5
Baseline perimeter estimate.
- 1Compute h then evaluate Ramanujan II
a=10, b=3
Elongated ellipse.
- 1Compute h=((7)/(13))²
- 2Evaluate full approximation
a=b=4
Circle case.
- 1h=0 so formula becomes 2πa
Introduction
Use Ramanujan’s second approximation for a highly accurate ellipse perimeter estimate.
Formula and Method
Ellipse Perimeter Calculator uses: h=((a-b)/(a+b))^2; perimeter ≈ π(a+b)(1 + 3h/(10 + √(4-3h)))
Enter all required inputs
Apply the underlying math formula(s)
Compute supporting terms where needed
Round numeric outputs for stable display
Input Fields
Provide values for: a, b.
- 1
a: a
- 2
b: b
Output Fields
The calculator returns: perimeter.
- 1
perimeter: Approximate ellipse perimeter (Ramanujan II)
Validation Rules
Input validation is applied before calculation to prevent invalid math states.
a and b must be finite and positive.
Perimeter output is an approximation.
Formula remains stable even for high eccentricity.
Output is rounded to 6 decimals.
How to Use This Calculator
Fill in the inputs, run the calculator, and review primary output first.
Enter the required values
Click calculate
Check the primary output
Use example scenarios for verification
Practical Uses
This calculator supports learning, quick checks, and day-to-day technical problem solving.
Homework and exam preparation
Engineering and science sanity checks
Classroom demonstrations
Fast recalculation with different inputs
FAQs
What does the Ellipse Perimeter Calculator compute?
Use Ramanujan’s second approximation for a highly accurate ellipse perimeter estimate.
Which inputs are required?
Required inputs: a, b.
How should I format numbers?
Use finite numeric values; decimals and negative numbers are allowed unless restricted by validation rules.
How are results rounded?
Numeric outputs are rounded to about 6 decimal places for readability.
Why might I see an error?
a and b must be finite and positive.
Can I use this for learning and verification?
Yes. Use the examples and formula section to verify manual calculations quickly.