Ellipse Calculator
Calculate ellipse area, perimeter, and eccentricity from semi-major and semi-minor axes.
Inputs
units
units
Results
Area
47.12
Perimeter25.53
Eccentricity0.8
How to Use This Calculator
- Enter the Semi-Major Axis (a) β the longer half-axis β and the Semi-Minor Axis (b) β the shorter half-axis.
- Area = Ο Γ a Γ b; when a = b the ellipse becomes a circle with radius a.
- Perimeter uses the Ramanujan approximation: Ο Γ (3(a+b) β β((3a+b)(a+3b))), which is accurate to within 0.5%.
- Eccentricity e = β(1 β bΒ²/aΒ²) ranges from 0 (circle) to just under 1 (very elongated ellipse).
- Focal distance c = β(aΒ²βbΒ²) gives the distance from center to each focus point.
- Both axes must be positive; a must be β₯ b (swap them if needed).
Ad Placeholder
Formula
Area = Οab, Perimeter β Ο(3(a+b) - β((3a+b)(a+3b)))Related Calculators
Circle Calculator
Calculate radius, diameter, circumference, area, sector area, and arc length of a circle from any known value.
Area Calculator
Calculate the area and perimeter of common shapes β rectangle, circle, triangle, trapezoid, and ellipse.
Perimeter Calculator
Calculate the perimeter of rectangles, circles (circumference), triangles, and regular polygons with any number of sides.
Ad Placeholder