How to Use Ellipse Calculator
The Ellipse Calculator makes it effortless to analyse any ellipse from two numbers.
- Enter Semi-Major Axis (a) — the longer radius measured from the center to the edge along the major axis.
- Enter Semi-Minor Axis (b) — the shorter radius measured along the minor axis. b must be ≤ a.
- Read results instantly — the Ellipse Calculator displays area, approximate perimeter, focal distance, eccentricity, foci coordinates, and the standard equation without any button press.
The Ellipse Calculator is useful for geometry homework, engineering drawing verification, astronomy (planetary orbits are elliptical), and optical lens design. Whenever you need accurate ellipse measurements in seconds, open the Ellipse Calculator.
Formula & Theory — Ellipse Calculator
The Ellipse Calculator applies the following standard formulas:
Area: A = π · a · b
Perimeter: C ≈ π · [3(a+b) − √((3a+b)(a+3b))] (Ramanujan)
Focal distance: c = √(a² − b²)
Eccentricity: e = c / a
Standard eq.: x²/a² + y²/b² = 1
Foci: (±c, 0)
| Symbol | Meaning |
|---|---|
| a | Semi-major axis (longest half-width) |
| b | Semi-minor axis (shortest half-height) |
| c | Distance from center to each focus |
| e | Eccentricity (0 = circle, → 1 = very flat) |
The exact ellipse perimeter requires an elliptic integral with no closed form, so the Ellipse Calculator uses the highly accurate Ramanujan approximation instead. For most practical purposes — from drafting to 3D modelling — the error is negligible.
When is the Ellipse Calculator most accurate?
The Ramanujan approximation used by this Ellipse Calculator has a maximum relative error below 0.5% across all valid a/b ratios. For nearly circular shapes (b ≈ a) the Ellipse Calculator is essentially exact.
Use Cases for Ellipse Calculator
The Ellipse Calculator covers a wide range of real-world scenarios:
- Academic geometry — verify textbook answers for ellipse area and perimeter problems using the Ellipse Calculator.
- Engineering drawing — quickly confirm dimensions when sketching elliptical flanges, pipe cross-sections, or oval cutouts.
- Astronomy — approximate orbital paths: Earth's orbit has a ≈ 149.6 million km and e ≈ 0.0167; the Ellipse Calculator handles these large numbers with ease.
- Art and design — scale elliptical frames or logo shapes while preserving proportions.
- Architecture — calculate the boundary length of elliptical rooms, arches, or decorative panels.
Whether you are a student, engineer, or designer, the Ellipse Calculator provides fast, reliable ellipse measurements entirely in your browser.