How to use the ellipse calculator
Find the area and perimeter (Ramanujan) of an ellipse. Enter semi-major axis a, semi-minor axis b in the fields above; the area, perimeter (approx.), eccentricity are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- a — Semi-major axis a
- b — Semi-minor axis b
Worked example
With semi-major axis a = 8, semi-minor axis b = 5, the calculator gives area ≈ 125.6637; perimeter (approx.) ≈ 41.38626; eccentricity ≈ 0.7806247.
Frequently asked questions
What is the formula for the ellipse calculation?
Area = π × a × b. Perimeter (approx.) = π × (3 × (a+b)-√((3 × a+b) × (a+3 × b))). Eccentricity = √(1-(b / a)^2). Here a is semi-major axis a, b is semi-minor axis b.
What inputs do I need for the ellipse calculator?
You need semi-major axis a, semi-minor axis b. 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 this 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 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.