Ellipse Eccentricity CalculatorFree online math calculator — instant results, no sign-up
Calculate eccentricity from semimajor and semiminor axes.
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About the Ellipse Eccentricity Calculator
Calculate eccentricity from semimajor and semiminor axes. Semimajor axis must be at least the semiminor axis.
- Semimajor axis
- Enter semimajor axis in units. Accepted minimum: 1e-06.
- Semiminor axis
- Enter semiminor axis in units. Accepted minimum: 0.
Formula and method
Result = sqrt(1 - (minor / major) ** 2)
- majorSemimajor axis (units)
- minorSemiminor axis (units)
Calculate eccentricity from semimajor and semiminor axes. Substitute the variables using the units defined above. Semimajor axis must be at least the semiminor axis.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Semimajor axis5 units
- Semiminor axis3 units
Results
- Result0.8
How to use the Ellipse Eccentricity Calculator
- 1Enter semimajor axis in units.
- 2Check semiminor axis.
- 3Read the numerical result and compare the stated assumptions with your situation.
Reading your result
Calculate eccentricity from semimajor and semiminor axes. The displayed quantity is dimensionless. A negative value, when the formula permits one, describes the direction of the difference—not a positive gain.
Limitations
Semimajor axis must be at least the semiminor axis. Numeric results are rounded for display; the calculation does not establish that your chosen inputs represent a realistic or permitted scenario.
Common questions
Which units does Ellipse Eccentricity require?+
Semimajor axis: units; Semiminor axis: units. Do not mix incompatible units.
What assumptions matter for Ellipse Eccentricity?+
Semimajor axis must be at least the semiminor axis.
How should I check a Ellipse Eccentricity result?+
Use the formula above with the shown starting inputs and compare the worked example generated from the tool. Check the original measurements and terms before using the figure.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.