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Calculators / Math / Ellipse eccentricity
Ellipse eccentricity calculator
Calculate ellipse eccentricity and focus spacing from its semi-axes.
On this page
Eccentricity0.8
Focus distance from centre4units
Distance between foci8units
Calculator controls
How to calculate
Calculate ellipse eccentricity and focus spacing from its semi-axes.
Eccentricity = sqrt(1-b^2/a^2); Focus distance from centre = sqrt(a^2-b^2) units; Distance between foci = 2*sqrt(a^2-b^2) units
Worked example
Semi-major axis: 5; Semi-minor axis: 3.
Eccentricity: 0.8 ; Focus distance from centre: 4 units; Distance between foci: 8 units.
Assumptions and limits
Enter semi-axes, not full diameters, using one length unit. The major semi-axis must be at least as long as the minor semi-axis; equal axes give a circle with zero eccentricity.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate ellipse eccentricity and focus spacing from its semi-axes.
When this tool is useful
Eccentricity = sqrt(1-b^2/a^2); Focus distance from centre = sqrt(a^2-b^2) units; Distance between foci = 2*sqrt(a^2-b^2) units
Understanding your inputs
| Input | What to enter |
|---|---|
| Semi-major axis | Enter a number of at least 1e-12 and no more than 1000000000000. |
| Semi-minor axis | Enter a number of at least 1e-12 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Enter semi-axes, not full diameters, using one length unit. The major semi-axis must be at least as long as the minor semi-axis; equal axes give a circle with zero eccentricity.
How is the result calculated?
Eccentricity = sqrt(1-b^2/a^2); Focus distance from centre = sqrt(a^2-b^2) units; Distance between foci = 2*sqrt(a^2-b^2) units