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Geometry

Ellipse Foci and Eccentricity Calculator

Find focal distance and eccentricity from an ellipse’s semimajor and semiminor axes.

Use consistent dimensionsArea and volume units explained below
Geometry desk
Geometry desk

Match each dimension to the shape and keep units consistent.

See the method

Set the dimensions

Runs on your device

Your measurement

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter semimajor axis, semiminor axis.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Center-to-focus distance c=sqrt(a²−b²); eccentricity e=c/a.

A WORKED EXAMPLE

Using semimajor axis = 5 units, semiminor axis = 3 units, the result is 4 units. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Axis inputs are half-lengths. For an ellipse centered at the origin with horizontal major axis, the foci are (±c,0).

What to keep in mind

Axis inputs are half-lengths. For an ellipse centered at the origin with horizontal major axis, the foci are (±c,0). Use the indicated units consistently. Ideal shapes are assumed; dimensions must describe the same object. Display rounding does not increase measurement precision.

Common questions

How do I use this ellipse foci and eccentricity calculator?

Find focal distance and eccentricity from an ellipse’s semimajor and semiminor axes. Enter semimajor axis in units, semiminor axis in units. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Axis inputs are half-lengths. For an ellipse centered at the origin with horizontal major axis, the foci are (±c,0).

Methodology maintained by ClarityKit. How these tools are built and checked.