🔵 Ellipse Area Calculator

Calculate the area of an ellipse from its semi-major and semi-minor axes.

Semi-major axis - Long radius (a) Semi-minor axis - Short radius (b)

What is an Ellipse?

An ellipse is the set of all points in a plane where the sum of distances from two fixed points F₁ and F₂ (foci) is constant. For any point P: |PF₁| + |PF₂| = 2a (major axis).

Area Calculation

S = π × a × b

S: Area | a: semi-major axis (long radius) | b: semi-minor axis (short radius)

Circumference Calculation

L ≈ 2π × √((a² + b²) / 2)

Lambert approximation — approximation of the exact integral value

The circumference of an ellipse has no simple formula like a circle. The formula above is the most commonly used approximation.

Focal Distance

c = √(a² − b²)

Distance between foci F₁ and F₂ = 2c

Eccentricity

e = c / a = √(1 − (b/a)²)

e = 0 is a circle, 0 < e < 1 is an ellipse. The closer e is to 1, the more elongated the ellipse.

Equation of an Ellipse

x² / a² + y² / b² = 1

Standard form ellipse centered at the origin. If a > b > 0, the major axis lies on the x-axis.