How to use the ellipse foci and eccentricity calculator
Find the focal distance and eccentricity of an ellipse from its semi-axes. Enter semi-major axis, semi-minor axis in the fields above; the focal distance from centre c, eccentricity are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “ellipse foci distance”, “ellipse eccentricity”, “focal length of ellipse”, “calculate ellipse foci and eccentricity”, “find focal distance from centre c”.
Formula
Variables
- a — Semi-major axis
- b — Semi-minor axis
Worked example
With semi-major axis = 5, semi-minor axis = 3, the calculator gives focal distance from centre c ≈ 4; eccentricity ≈ 0.8.
Frequently asked questions
What is the ellipse foci and eccentricity calculator used for?
Find the focal distance and eccentricity of an ellipse from its semi-axes. It helps with questions such as “ellipse foci distance”, “ellipse eccentricity”, “focal length of ellipse”.
What is the formula for the ellipse foci and eccentricity calculation?
Focal distance from centre c = √(a × a-b × b). Eccentricity = √(a × a-b × b) / a. Here a is semi-major axis, b is semi-minor axis.
What inputs do I need for the ellipse foci and eccentricity calculator?
You need semi-major axis, semi-minor axis. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the ellipse foci and eccentricity calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the ellipse foci and eccentricity result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.