Ellipse Calculator
MathCalculate the eccentricity, area, perimeter, and foci of an ellipse from its semi-major and semi-minor axes.
Area
Area of the ellipse.
Perimeter
25.5270
Perimeter, using Ramanujan's approximation.
Eccentricity
0.8000
How elongated the ellipse is, from 0 (a circle) to just under 1.
Foci Distance from Center
4.0000
Distance from the center to each focus.
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Odeh Ahwal0people find this calculator helpful
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Frequently Asked Questions
Why does the perimeter use an approximation instead of an exact formula?
Unlike a circle, an ellipse has no simple closed-form formula for its exact perimeter, it requires a special mathematical function called an elliptic integral. Ramanujan's approximation is extremely accurate for nearly all practical purposes and is the standard formula used for ellipse perimeter calculators.
What does eccentricity mean?
Eccentricity measures how stretched an ellipse is, from 0 for a perfect circle up toward 1 for an increasingly elongated shape. It is calculated from how much smaller the semi-minor axis is compared to the semi-major axis.
How is this different from the dedicated Ellipse Area and Ellipse Perimeter calculators?
This is the comprehensive version that computes area, perimeter, eccentricity, and foci distance all together. The dedicated calculators exist as narrower, more specifically-titled pages for visitors who only need one of these values.
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