Ellipse Eccentricity Calculator

Work out ellipse eccentricity instantly with clear inputs, formula shown and shareable results.

About Ellipse Eccentricity Calculator

Eccentricity measures how far an ellipse departs from a circle: e = c/a with c = √(a² − b²). e = 0 is a circle and e → 1 is an infinitely stretched ellipse.

Formulas

Eccentricity

e = √(a² − b²) / a = c / a

Semi-latus rectum

ℓ = b² / a

Worked example

With the default values below, Ellipse Eccentricity Calculator returns Eccentricity e of 0.80000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Semi-major axis aminimum 0: 5
Semi-minor axis bminimum 0: 3

Results

Eccentricity e: 0.80000000
Centre-to-focus distance c: 4.0000
Distance between foci: 8.0000
Semi-latus rectum b²/a: 1.8000

Step by step

1Values used
2Eccentricity
3Semi-latus rectum
4Eccentricity e= 0.80000000
5Centre-to-focus distance c= 4.0000
6Distance between foci= 8.0000
7Semi-latus rectum b²/a= 1.8000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is Earth's orbital eccentricity?

About 0.0167, which is why the orbit looks almost circular.

What if I enter b larger than a?

The two axes are swapped automatically so that a is always the semi-major axis.