Enter ellipse dimensions
Formula used
Full outer ellipse area: A = πab, where a is the semi-major axis and b is the semi-minor axis.
Inner void area: Ainner = πaibi. Use this only when inner dimensions are provided.
Net full area: Anet = Aouter - Ainner.
Sector area: Asector = Anet × (θ / 360), where θ is the selected angle in degrees.
Total selected area: Atotal = Asector × quantity.
Perimeter estimate: Ramanujan’s second approximation, P ≈ π(a+b)[1 + 3h / (10 + √(4 - 3h))], with h = ((a-b)² / (a+b)²).
Eccentricity: e = √(1 - b²/a²). A value nearer 0 is rounder, while a value nearer 1 is more stretched.
How to use this calculator
- Choose whether you want to enter semi-axes or full diameters.
- Enter the outer major and minor dimensions for the ellipse.
- Optionally enter inner dimensions to subtract a hollow center.
- Set the sector angle when you need only part of the ellipse.
- Add quantity and a scale factor when several identical shapes are needed.
- Click the calculate button to display the result panel above the form.
- Use the CSV or PDF buttons to export the current result summary.
- Review the graph to visually confirm the outer and inner ellipse proportions.
Example data table
| Scenario | Input mode | Outer major | Outer minor | Inner major | Inner minor | Angle | Quantity | Scale | Net full area | Total selected area |
|---|---|---|---|---|---|---|---|---|---|---|
| Solid ellipse | Semi-axes | 12 cm | 8 cm | 0 | 0 | 360° | 1 | 1.00 | 301.59 cm² | 301.59 cm² |
| Half ellipse | Semi-axes | 10 cm | 6 cm | 0 | 0 | 180° | 1 | 1.00 | 188.50 cm² | 94.25 cm² |
| Elliptical ring | Diameters | 30 cm | 18 cm | 18 cm | 10 cm | 360° | 1 | 1.00 | 282.74 cm² | 282.74 cm² |
| Scaled production set | Semi-axes | 7 m | 4 m | 0 | 0 | 270° | 6 | 1.20 | 126.67 m² | 570.03 m² |
FAQs
1. What dimensions should I enter?
Use the outer major and minor values for the full ellipse. If you switch to diameter mode, enter full diameters. If you stay in semi-axis mode, enter half-lengths from center to edge.
2. What happens if my major value is smaller than my minor value?
The calculator automatically reorders the dimensions so the larger value becomes the semi-major axis. This keeps eccentricity, focus distance, and perimeter estimates mathematically correct.
3. Can I calculate only part of an ellipse?
Yes. Enter a sector angle between 0 and 360 degrees. The calculator multiplies the net full area by that angle fraction, then applies the quantity value.
4. Why are there inner dimensions?
Inner dimensions let you subtract a hollow center. This is useful for elliptical frames, gaskets, tracks, and ring-shaped parts where material area matters more than outer coverage.
5. Is the perimeter exact?
No. Ellipse perimeter has no simple exact elementary formula, so this tool uses Ramanujan’s highly accurate approximation. It is widely accepted for practical engineering and geometry work.
6. What does the scale factor change?
The scale factor changes all dimensions uniformly before results are calculated. Areas change with the square of the scale, while perimeter and diameters change linearly.
7. What unit label should I use?
Enter any short unit such as mm, cm, m, in, or ft. The calculator appends that label to linear values and automatically shows squared units for areas.
8. What can I do with the export buttons?
The CSV button downloads a simple metric table for spreadsheets. The PDF button creates a compact report of the current inputs and results for sharing or printing.