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Ellipse Perimeter and Area Calculator — result sheet
Estimate an ellipse’s perimeter with Ramanujan’s approximation and calculate its area and eccentricity.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: h = ((a-b)/(a+b))²; perimeter ≈ π(a+b)(1 + 3h/(10+√(4-3h))); area = πab; e = √(1-b²/a²).
An ellipse has no elementary exact perimeter formula. This page uses a high-accuracy Ramanujan approximation while retaining the exact area and eccentricity relationships.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Semi-major axis a — units; minimum 1.0E-6; maximum 1000000000
- Semi-minor axis b — units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Semi-major axis a | 5 |
| Semi-minor axis b | 3 |
Perimeter: about 25.53 units; area: about 47.12 square units; eccentricity: 0.80.
Assumptions and limits
- a is the semi-major axis and must be at least as large as b, the semi-minor axis.
- The perimeter is an approximation; for high-precision surveying or engineering work, use a validated elliptic-integral implementation.
- Both axes use one unit, area uses squared units, and eccentricity is dimensionless.
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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