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Area of an Ellipse Calculator.

Calculates the area of an ellipse given its semi-major and semi-minor axes.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Measure the semi-major axis (a) and semi-minor axis (b) of the ellipse.

  2. 2

    Multiply a by b.

  3. 3

    Multiply the result by π (approximately 3.14159).

  4. 4

    The result is the area in square units.

pi * semi_major * semi_minor

Frequently asked questions

What is the difference between semi-major and semi-minor axes?

The semi-major axis is the longest radius from the center to the edge, and the semi-minor axis is the shortest radius. They are perpendicular to each other.

Can I use this calculator for a circle?

Yes, if a = b, the ellipse is a circle and the formula gives πr², which is the area of a circle.

What units should I use?

Any consistent unit (e.g., meters, feet, inches). The area will be in square units of that same unit.

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Results

Formula checked

Area

47,124sq units

Ask Anything

Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Calculates the area of an ellipse given its semi-major and semi-minor axes.

  1. Measure the semi-major axis (a) and semi-minor axis (b) of the ellipse.
  2. Multiply a by b.
  3. Multiply the result by π (approximately 3.14159).
  4. The result is the area in square units.

Formulas

The math behind this calculator, written out so you can verify the result.

Area of an Ellipse

A = π × a × b

The area is the product of π, the semi-major axis (a), and the semi-minor axis (b).

Example:

Input: a = 5, b = 3

Calculation: π × 5 × 3

Result: ≈ 47.12 square units

Real-world use cases

Where this calculation shows up in everyday life.

Architecture and design

Calculate the floor area of elliptical rooms, domes, or decorative elements.

Example: An elliptical garden with axes 8m and 5m has an area of about 125.66 m².

Engineering

Determine cross-sectional areas of elliptical pipes or tanks for fluid capacity.

Example: An elliptical duct with semi-axes 0.3m and 0.2m has an area of about 0.1885 m².

Astronomy

Estimate the area of elliptical orbits or planetary features.

Example: An orbit with semi-major 1 AU and semi-minor 0.98 AU has an area of about 3.08 AU².

Tips and common mistakes

Tips

  • Ensure both axes are measured in the same unit.
  • If you only have the full axes (diameters), divide each by 2 to get the semi-axes.
  • For a circle, set both axes equal to the radius.
  • Use more precise values of π for critical calculations.

Common Mistakes to Avoid

  • Using the full axes instead of the semi-axes.
  • Forgetting to multiply by π.
  • Mixing units (e.g., meters and centimeters) without conversion.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.