Ellipse Calculator – Area, Axes and Foci
Find ellipse area, full axis lengths, center-to-focus distance and eccentricity from its two semiaxes.
Formula
A=πab; c=√(L²−S²); e=c/L; L=max(a,b), S=min(a,b)
First semiaxis: 5 cm · Second semiaxis: 3 cm · Area ≈ pi×(5 cm × 0.01 m/cm)×(3 cm × 0.01 m/cm)×10000 · Major axis ≈ 2×max((5 cm × 0.01 m/cm),(3 cm × 0.01 m/cm))×100 · Minor axis ≈ 2×min((5 cm × 0.01 m/cm),(3 cm × 0.01 m/cm))×100 · Center to focus ≈ sqrt((max((5 cm × 0.01 m/cm),(3 cm × 0.01 m/cm))-min((5 cm × 0.01 m/cm),(3 cm × 0.01 m/cm)))×(max((5 cm × 0.01 m/cm),(3 cm × 0.01 m/cm))+min((5 cm × 0.01 m/cm),(3 cm × 0.01 m/cm))))×100 · Eccentricity ≈ (4)÷(max((5 cm × 0.01 m/cm),(3 cm × 0.01 m/cm))×100)
How to use
- Enter both semiaxis lengths, not full diameters.
- Choose the unit for each length.
- Read area in cm² and lengths in cm.
Examples
- a=5 cm, b=3 cm: A=15π cm², c=4 cm, e=0.8.
Frequently asked questions
Must a be the longer semiaxis?
No. Either order works.
What is the focal distance?
The distance from the center to one focus. The two foci are 2c apart.
What if both semiaxes are equal?
The ellipse is a circle and its eccentricity is zero.
Sources
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