Last updated October 10, 2026 · Report an error
Unlike a circle, an ellipse has no single "radius" — it's defined by two axes, and while its area has a clean exact formula, its circumference does not: there's no elementary closed-form expression for it, only very accurate approximations.
This calculator finds the exact area and an approximate circumference (using Ramanujan's well-known second approximation) from an ellipse's semi-major and semi-minor axes.
How it works
Enter the semi-major axis (a, the longer radius) and semi-minor axis (b, the shorter radius). The calculator finds the area using the exact formula π·a·b, and estimates the circumference using Ramanujan's second approximation, which is accurate to a tiny fraction of a percent for virtually any realistic ellipse shape.
- Enter semi-major axis (a).
- Enter semi-minor axis (b).
- Click Calculate to see your results.
Examples
An ellipse with axes 5 and 3
An ellipse with a semi-major axis of 5 and semi-minor axis of 3 has an exact area of about 47.12, and an approximate circumference of about 25.53.
Who should use it
- Calculating the area of an elliptical garden bed, table, or room.
- Estimating material needed to border an elliptical shape, like edging or trim.
Industry applications
- Landscaping and garden design
- Engineering and manufacturing design
Advantages
- Uses the exact formula for area and a highly accurate approximation for circumference.
- Includes a complete, formula-based step-by-step solution.
Limitations
- Circumference is always an approximation, since no exact elementary formula exists.
Common mistakes to avoid
- Using the full major and minor axis lengths (diameters) instead of the semi-axes (half-lengths) that the formulas require.
- Expecting an exact circumference value — remember it's always an approximation, just an extremely accurate one.
Best practices
- Double check whether you have the full axis lengths or the semi-axis (half) lengths before entering values — this is the most common source of error.
Tips
- If you only have the full width and height of an elliptical object, divide each by 2 first to get the semi-major and semi-minor axes before entering them here.