Ellipse / Oval Area Calculator
Calculate the area, perimeter, eccentricity, and focal distance of an ellipse or oval from its semi-major and semi-minor axes, or solve for a missing axis from a known area.
An ellipse’s area (also called an oval’s area) depends on two independent measurements — a semi-major axis and a semi-minor axis — unlike a circle, where the radius alone determines everything. This calculator finds the area, perimeter, eccentricity, and focal distance from both semi-axes, and includes a mode most other ellipse calculators skip: solving for a missing axis when you already know the area and just one axis.
Enter your two semi-axes for the full set of results, or switch to the reverse mode if you know the area and need to find the other axis.
Ellipse Area Formula
Area = π × a × b
Where:
a = the semi-major axis (half the length of the ellipse’s longer diameter)
b = the semi-minor axis (half the length of the ellipse’s shorter diameter)
This is a direct extension of a circle’s Area = πr² formula — a circle is just an ellipse where a and b happen to be equal, so π × a × b reduces to πr² in that special case.
Worked Example: An Oval Garden Bed
A garden bed shaped like an oval with a 6-ft semi-major axis and a 4-ft semi-minor axis: Area = π × 6 × 4 ≈ 75.40 square feet.
Perimeter, Eccentricity, and Focal Distance
Along with the area, this calculator’s main mode also returns three related measurements for the same ellipse.
Perimeter (Approximate)
Unlike a circle’s circumference, an ellipse has no exact elementary formula for its perimeter — it can only be expressed exactly using an infinite series or elliptic integrals. This calculator uses Ramanujan’s second approximation, which stays highly accurate for most real-world ellipses and only loses precision for very elongated (high-eccentricity) shapes.
Worked Example
For the same 6-ft by 4-ft semi-axis ellipse above: Perimeter ≈ 31.73 feet.
Eccentricity
Eccentricity = √(1 − (b/a)²)
Eccentricity measures how elongated an ellipse is, on a scale from 0 (a perfect circle) approaching 1 (an increasingly flattened, stretched-out shape). It has no unit — it’s a pure ratio.
Worked Example
For a = 6 ft and b = 4 ft: Eccentricity = √(1 − (4/6)²) = √(1 − 0.4444) ≈ 0.75.
Focal Distance
Focal Distance (c) = √(a² − b²)
Every ellipse has two foci, symmetric points along the major axis such that the sum of the distances from any point on the ellipse to both foci is constant. The focal distance is how far each focus sits from the ellipse’s center.
Worked Example
For a = 6 ft and b = 4 ft: Focal Distance = √(6² − 4²) = √(36 − 16) = √20 ≈ 4.47 feet.
Finding a Missing Axis From a Known Area
Known Axis × Missing Axis = Area ÷ π, so Missing Axis = Area ÷ (π × Known Axis)
This reverses the area formula: if you already know the ellipse’s area and one of its two semi-axes, this mode solves for the other one directly — a mode most other ellipse calculators don’t offer, since they typically only compute forward from both axes to the area rather than backward from area plus one axis.
Worked Example
An elliptical pool cover needs to be 50 square feet, and the pool’s semi-minor axis is 5 ft: Missing Axis = 50 ÷ (π × 5) ≈ 3.18 feet, giving a semi-major axis of about 3.18 feet.
Frequently Asked Questions
How do I calculate the area of an oval?
An oval and an ellipse use the same formula: Area = π × a × b, where a and b are the semi-major and semi-minor axes (half the length and half the width, measured through the center). A 6-ft by 4-ft semi-axis oval has an area of about 75.40 square feet.
What’s the difference between the semi-major axis and the full major axis?
The major axis is the ellipse’s full longer diameter, end to end. The semi-major axis is half of that — the distance from the center to the edge along the longer direction. This calculator asks for the semi-axis values, not the full diameters.
Why doesn’t this calculator give an exact perimeter?
An ellipse’s perimeter has no exact elementary formula — it requires an infinite series or elliptic integrals to compute precisely. This calculator uses Ramanujan’s second approximation, which is accurate to a very small fraction of a percent for most ellipses and is the same approach used by other engineering and math calculators.
What does an eccentricity of 0 or close to 1 mean?
An eccentricity of 0 means the ellipse is actually a perfect circle (the two axes are equal). As eccentricity increases toward 1, the ellipse becomes progressively more elongated and flattened.