The Ellipse Area Calculator helps you find the area, perimeter, and eccentricity of any ellipse — using semi-major & semi-minor axes, full diameters, or eccentricity.
It supports all common units (inches, feet, centimeters, and meters) and provides instant results with precise π (3.1416) calculations.

• Supports multiple input modes: semi-axes (a, b), axes (A, B), or semi-major + eccentricity.
• Accurate results based on Ramanujan’s perimeter approximation formula.
• Instantly converts and copies output for easy documentation or reuse.
• Ideal for geometry, architecture, astronomy, and design projects.

Keywords: area of an ellipse, ellipse area calculator, ellipse area formula, perimeter of ellipse, eccentricity of ellipse.

The area of an ellipse depends on its two radii — the semi-major axis (a) and the semi-minor axis (b).
Below are the main formulas used in geometry and engineering to calculate it accurately.

1. Standard Formula:
A = π × a × b
where a = semi-major axis, and b = semi-minor axis.

2. Using Diameters:
A = π × (A/2) × (B/2)
Here, A and B are the full major and minor diameters of the ellipse.

3. Using Eccentricity (e):

b = a × √(1 – e²) → A = π × a² × √(1 – e²)

This method is useful when the ellipse’s eccentricity is known instead of the minor axis.

The perimeter of an ellipse—also called the circumference of an ellipse—does not have a simple exact formula because it involves elliptic integrals.
However, for nearly all practical applications, a highly accurate approximation developed by the mathematician S. Ramanujan is used.

Ramanujan’s Approximation:

P ≈ π [3(a + b) – √((3a + b)(a + 3b))]

This formula delivers an error margin of less than 0.5% for most real-world ellipses,
making it ideal for engineering, astronomy, and CAD design purposes.

Keywords: perimeter of ellipse, circumference of ellipse, ellipse circumference formula.

Below are a few ellipse area and perimeter examples using different known parameters. These examples illustrate how the calculator adapts to inputs in various units or forms:

• ① a = 8 in, b = 5 in →
  A = π × 8 × 5 = 125.66 in²,
  P ≈ 41.39 in
• ② A = 16 cm, B = 10 cm →
  A = π × 8 × 5 = 125.6 cm²,
  e = 0.781
• ③ a = 12 m, e = 0.5 →
  b = 12 × √(1 – 0.25) = 10.39 →
  A ≈ 392.7 m²

Keywords: area of an ellipse example, perimeter of ellipse example, ellipse calculator.

This quick-reference table converts ellipse area and perimeter values across common measurement units — inches, centimeters, and square conversions.
It helps visualize how results change depending on the selected unit.

Keywords: ellipse area converter, area of ellipse in cm², square inches to cm².

The Ellipse Area Calculator is not just for math exercises — it’s widely applicable across several professional and educational domains. Here are the most common uses:

• Geometry & Education: Perfect for demonstrating how area, perimeter, and eccentricity interact in ellipse shapes through visual examples.
• Architecture: Used in designing domes, arches, windows, and other curved structures requiring precise area and proportion measurements.
• Astronomy: Essential for analyzing elliptical orbits of planets, satellites, and celestial bodies.
• Design & Printing: Helpful for calculating aspect ratios and maintaining proportional balance in logos, graphics, and visual layouts.

Keywords: geometry ellipse, astronomy ellipse, ellipse shape design.

Even simple ellipse calculations can go wrong due to minor mix-ups. Here are the most frequent mistakes users make — and how to avoid them:

• 🔹 Confusing axes (A, B) with semi-axes (a, b): Remember that a = A/2 and b = B/2; using full diameters directly will double your area result.
• 🔹 Forgetting to convert between diameter and radius halves: Always confirm whether the given value represents a full axis or a semi-axis before applying the formula.
• 🔹 Using the circle formula (πr²) instead of ellipse (πab): The circle formula only applies when a = b; otherwise, the ellipse formula must be used.
• 🔹 Mixing different unit systems (inches/cm): Be consistent — converting all inputs to the same unit prevents major discrepancies in results.

Keywords: ellipse area error, ellipse formula confusion, measurement tips.

1) What is the formula for the area of an ellipse?
The standard formula is A = πab, where a is the semi-major axis and b is the semi-minor axis. If you have full diameters A and B, use A = π(A/2)(B/2).

2) What is the difference between a and b in ellipse?
a is the longer radius (semi-major axis) and b is the shorter radius (semi-minor axis). By convention, a ≥ b.

3) What is eccentricity in an ellipse?
Eccentricity e measures how “stretched” an ellipse is: e = √(1 − b²/a²). A circle has e = 0; as e → 1, the ellipse becomes more elongated.

4) How do you find the perimeter of an ellipse?
There’s no simple closed-form in elementary functions (it involves elliptic integrals). This calculator uses Ramanujan’s approximation:
P ≈ π[3(a + b) − √((3a + b)(a + 3b))], which is highly accurate for most ellipses.

5) What happens if a = b (is it a circle)?
Yes. The ellipse becomes a circle of radius r = a = b, so Area = πr² and Circumference = 2πr.

6) How to calculate area using integration?
Using symmetry, A = 4∫₀ᵃ b√(1 − x²/a²) dx. Evaluating this integral yields A = πab.

7) What is the surface area of an ellipse?
“Surface area” applies to 3D shapes. A 2D ellipse has area (πab), not surface area. If you meant a 3D ellipsoid, formulas differ (there’s no simple closed form; approximations are used).

• Area: A = πab (or A = π(A/2)(B/2) using diameters).
• Perimeter: Calculated with Ramanujan’s approximation for practical accuracy.
• Eccentricity: e = √(1 − b²/a²) indicates how stretched the ellipse is.
• Units: Supports inches, feet, centimeters, and meters—be consistent when converting.
• Circle case: If a = b, the ellipse becomes a circle with Area = πr².

Need similar shapes? See the related tools below.

• Circle Area Calculator → for perfect circles
• Rectangle Area Calculator → for right angles
• Triangle Area Calculator → for 3-sided shapes
• Trapezoid Area Calculator → for parallel sides