Ellipse Area Calculator
From the two semi-axes, get the area and the circumference — the numbers that describe any oval, from a dining table to a planetary orbit.
Two semi-axes, two answers
Enter the semi-major axis (a) and semi-minor axis (b) and the calculator returns the area (πab) and the circumference at once.
Use halves, not full widths
The semi-axes are halves of the long and short diameters — a 10-by-6 oval has a = 5 and b = 3, not 10 and 6.
What is an ellipse area calculator?
Two semi-axes in, full ellipse out
An ellipse area calculator turns two measurements — the semi-major axis a and the semi-minor axis b — into the figures that describe an oval: the space it encloses and the distance around its edge. The semi-axes are half the longest and shortest diameters, measured from the centre out to the edge. That makes them the two inputs you need for oval tables and mirrors, running tracks, elliptical gardens and ponds, and the orbits of planets, which trace ellipses with the Sun at one focus. When the two semi-axes are equal, the ellipse is simply a circle.
Enter the two semi-axes in any length unit to get the area and circumference instantly.
The area is exact and simple; the circumference uses a famous approximation.
area = π × a × bThe area is π × a × b: multiply the two semi-axes together, then multiply by π (about 3.14159). The circumference has no simple exact formula — the precise value needs an elliptic integral — so this tool uses Ramanujan's approximation, π × [3(a + b) − √((3a + b)(a + 3b))], which is accurate to within a tiny fraction of a percent for ordinary shapes.
Suppose you have an ellipse with a semi-major axis of 5 and a semi-minor axis of 3.
Area
π × 5 × 3 = π × 15 = 47.123890 square units — the space inside.
Circumference
π × [3(5 + 3) − √((3·5 + 3)(5 + 3·3))] = 25.526986 — the distance around the edge.
Sanity check
The full diameters are 10 and 6, so the oval is wider than it is tall — and its area sits between a 10-wide and a 6-wide circle.
The two outputs answer two different everyday questions. The area (about 47.123890 square units for a = 5, b = 3) is the surface you cover — the glass on an oval table, the soil in an elliptical garden bed, the felt on a racetrack infield. The circumference (about 25.526986) is the distance once around the edge — the trim you would run around an oval mirror or the length of one lap. The single most common mistake is using the full diameters instead of the semi-axes: the axes are halves, so an oval measuring 10 across and 6 tall has a = 5 and b = 3, not 10 and 6, and feeding in the full widths quadruples the area. A second insight is the link to the circle: when a equals b, the ellipse becomes a circle of radius r, the area π × a × b collapses to π × r², and the circumference reduces to 2 × π × r. So a circle is just a perfectly symmetric ellipse, and reasoning about ovals is reasoning about stretched circles.
The area is exact, but the circumference and your inputs deserve a second look.
Approximate perimeter and consistent units
The circumference is Ramanujan's approximation, not an exact value — it is extremely close for ordinary ovals but drifts slightly for very long, thin ellipses where one axis dwarfs the other. The semi-axes are also unit-agnostic, so the answers are only meaningful if you keep one unit across both inputs: semi-axes in centimetres give a circumference in centimetres and an area in square centimetres, never a mix.