Math

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Ellipse Calculator.

Calculate ellipse area, focal distance, and eccentricity from its semi-axes.

On-device calculationNo signup
01

Set your values

Results update as you type.

area: 125.66370614

area

0.00000000
focalDistance: 6.244998

focalDistance

0.00000000
eccentricity: 0.78062475

eccentricity

0.00000000

Results update automatically as you type.

Calculate ellipse area, focal distance, and eccentricity from its semi-axes.

Use Cases

Geometry homework and exam prep

Quickly verify your manual calculations for ellipse area, focal distance, and eccentricity. Ideal for students learning conic sections.

Example: Check your answer for an ellipse with a=5 and b=3.

Design and engineering layouts

Determine key dimensions of elliptical shapes used in architecture, mechanical parts, or graphic design without complex math.

Example: Find the focal points for an elliptical arch with axes 10 and 6.

Frequently Asked Questions

How do I calculate the area of an ellipse?
Enter the semi-major axis (a) and semi-minor axis (b) into the calculator. The area is computed using the formula A = π × a × b. The result is displayed instantly.
What is the focal distance of an ellipse?
The focal distance is the distance from the center to each focus. It is calculated as c = √(a² - b²), where a is the semi-major axis and b is the semi-minor axis. Enter both axes to get the focal distance.
How is eccentricity determined?
Eccentricity (e) measures how elongated the ellipse is. It is calculated as e = c / a, where c is the focal distance and a is the semi-major axis. The calculator computes this automatically after you input the axes.

Tips & Common Mistakes

Tips

  • Ensure the semi-major axis is the longer of the two axes; the calculator assumes a ≥ b for correct focal distance and eccentricity.
  • Use consistent units for both axes (e.g., both in meters or both in inches) to get accurate results.
  • The focal distance and eccentricity are only defined for ellipses, so both axes must be positive numbers.
  • For a circle (a = b), the focal distance is 0 and eccentricity is 0, which the calculator will show.

Common Mistakes to Avoid

  • Swapping the semi-major and semi-minor axes, which can lead to incorrect focal distance and eccentricity values.
  • Entering negative numbers or zero for the axes; these are invalid because an ellipse requires positive dimensions.
  • Forgetting to use the same units for both axes, which can distort the area and other results.

Last updated: August 13, 2026