Axis-Aligned Ellipse Calculator
Axis-Aligned Ellipse: calculate results from explicit inputs, with a formula and worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Euclidean geometry. Use one consistent length unit; areas and volumes use its square and cube. Degenerate shapes are rejected. Very thin shapes may lose floating-point precision. Axes are parallel to coordinate axes; rotated conics are not included.
Example Calculation
- Horizontal semiaxis: 5 units
- Vertical semiaxis: 3 units
- Center h: 0
- Center k: 0
Horizontal semiaxis 5, vertical semiaxis 3, center (0,0) give foci (−4,0), (4,0) and area 15π.
Frequently asked questions
How do I use this calculator?
Enter horizontal semiaxis, vertical semiaxis, center h, center k. The result updates automatically. Use Reset to restore the example values.
What method does it use?
(x−h)²/a²+(y−k)²/b²=1; area=πab; focal distance=√|a²−b²|. Euclidean geometry. Use one consistent length unit; areas and volumes use its square and cube. Degenerate shapes are rejected. Very thin shapes may lose floating-point precision. Axes are parallel to coordinate axes; rotated conics are not included.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.