Ellipse Area Calculator — π × a × b
Enter the two semi-axes of an ellipse — a (semi-major) and b (semi-minor) — and instantly get the exact area using the formula A = π × a × b, along with how the area compares to the enclosing circle.
Area = π × a × b (square units)
- 1
Semi-axes
a = 6, b = 4 - 2
π × a
π × 6 = 18.849556 - 3
Area = π × a × b
18.849556 × 4 = 75.3982The ellipse area formula is exact — unlike the perimeter, it has a clean closed form.
How does this calculator work?
The area of an ellipse is A = π × a × b, where a is the semi-major axis and b is the semi-minor axis. It is the only ellipse formula with an exact closed form — no approximation needed. A circle (a = b = r) is the special case giving πr².
Formula
How this is calculated
An ellipse is the set of all points where the sum of distances from two fixed points (foci) is constant. Its shape is defined by two semi-axes: a, the half-length of the longer axis, and b, the half-length of the shorter axis. When a = b the ellipse becomes a circle with area πr², and the general formula π × a × b reduces to that familiar result.
The area formula A = π × a × b is exact — unlike the perimeter, the area of an ellipse has a clean closed form. It follows from the standard integral of the ellipse equation (x/a)² + (y/b)² = 1, evaluated over the interior, which gives exactly π × a × b.
Note that a and b are the semi-axes (half the full width and height), not the full diameters. If you measured the total width as 2a = 12 and total height as 2b = 8, the semi-axes are a = 6 and b = 4, giving A = π × 6 × 4 ≈ 75.40 square units.
Frequently asked questions
The major axis is the full longest diameter of the ellipse, running through both foci. The semi-major axis (a) is half that length — the distance from the centre to one end of the major axis. This calculator uses semi-axes (a and b), so enter half the total width and half the total height.
The area integral over an ellipse region factors neatly into π × a × b. The arc-length integral for the perimeter involves an elliptic integral, which cannot be expressed in terms of elementary functions — so every perimeter formula is either an approximation or defined by a special function.
If your ellipse is in standard form (x/a)² + (y/b)² = 1, the semi-axes are already a and b. In the expanded form Ax² + By² = C, the semi-axes are a = √(C/A) and b = √(C/B). Use the ellipse standard-form calculator for a full breakdown of general equations.
Also known as
TG we-Calculate Editorial Team. (2026). Ellipse Area Calculator — π × a × b [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/ellipse-area-calculator
TG we-Calculate Editorial Team. "Ellipse Area Calculator — π × a × b." TG we-Calculate. 2026. https://we-calculate.com/calculator/ellipse-area-calculator.
TG we-Calculate Editorial Team, "Ellipse Area Calculator — π × a × b," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/ellipse-area-calculator
@misc{wecalculate_ellipse_area_calculator, title = {Ellipse Area Calculator — π × a × b}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/ellipse-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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