Ellipse Table: Area by Semi-major axis (a)
Reference table of area for Ellipse across a range of semi-major axis (a) values — exact, engine-computed figures you can read off at a glance.
Ellipse Calculator
Verified formula Updated Jun 2026 Private — runs on your device
Verified formula
Private
Area
47.1239
- Circumference (approx.)
- 25.5270
For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.
How to use the Ellipse Calculator
The Ellipse Calculator works out your area, along with 1 related figure in an instant. Enter semi-major axis (a) and semi-minor axis (b) and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.
- Enter the semi-major axis (a).
- Enter the semi-minor axis (b).
- Read off your area, together with circumference (approx.) — the calculator updates automatically, with no button to press.
Formula
The Ellipse Calculator uses the formula:
Area = 3.141592653589793 × Semi-major axis (a) × Semi-minor axis (b)
Worked example
For example, with semi-major axis (a) of 5 units and semi-minor axis (b) of 3 units, the area is 47.1239.
| Semi-major axis (a) | 5 units |
|---|---|
| Semi-minor axis (b) | 3 units |
| Area | 47.1239 |
|---|---|
| Circumference (approx.) | 25.5270 |
Results are estimates for educational use, not professional advice.
Key terms explained
- Circumference
- The distance around the edge of a circle, equal to 2 × π × radius.
- Area
- The amount of two-dimensional space a shape covers, measured in square units.
Frequently asked questions
Multiply pi by both semi-axes: A = π × a × b. For a = 5 and b = 3 the area is about 47.12 square units.
An ellipse's exact perimeter has no simple closed formula. This calculator uses Ramanujan's well-known approximation, which is extremely accurate for most shapes.
The semi-major axis is half the longest diameter and the semi-minor axis is half the shortest. When they are equal the ellipse becomes a circle.
The ellipse becomes a circle of radius a, the area becomes πa² and the perimeter becomes 2πa.
The Ellipse Calculator uses the formula: Area = 3.141592653589793 × Semi-major axis (a) × Semi-minor axis (b). For example, with semi-major axis (a) of 5 units and semi-minor axis (b) of 3 units, the area is 47.1239.
Enter the semi-major axis (a). Enter the semi-minor axis (b). Read off your area, together with circumference (approx.) — the calculator updates automatically, with no button to press.
Related guides
How to Calculate Ellipse: Formula, Steps & Examples
Learn how to calculate Ellipse — the formula explained step by step, with worked examples and a free calculator to check your answer.