Ellipse Area Calculator
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Ellipse area formula explained
The area of an ellipse is A = π × a × b. The value a is one semi-axis and b is the other semi-axis. A semi-axis is half the full width or height of the ellipse.
Use this calculator for oval tables, tracks, decorative shapes, lenses, garden beds, or design layouts where the shape is an ellipse rather than a perfect circle.
Worked example: semi-axes 6 in and 4 in
A = π × a × b
A = π × 6 × 4
Result: 75.3982 in²
Full width versus semi-axis
If the ellipse is 20 cm wide and 12 cm tall, the semi-axes are 10 cm and 6 cm. Use those half measurements in the calculator, not the full width and full height.
Common mistakes
- Entering the full major and minor diameters instead of half values.
- Assuming an ellipse uses the same formula as a circle.
- Mixing measurements from different units.
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Step-by-step method
- Measure the full width and divide by two to get one semi-axis.
- Measure the full height and divide by two to get the other semi-axis.
- Multiply the two semi-axes together.
- Multiply the result by pi.
Second example: full size 30 in by 18 in
The semi-axes are 15 in and 9 in.
A = π × 15 × 9
Result: 424.1150 in²
Practical interpretation
Ellipse area is useful whenever a shape is oval rather than circular. The formula assumes a true mathematical ellipse. Real objects may be slightly irregular, but the calculation is usually a strong estimate for design, planning, and comparison.
For layout work, measure the longest full width and the shortest full width through the center. Then use half of each measurement as the calculator inputs.
How to calculate this measurement
An ellipse is like a stretched circle. Its area uses two radii: the semi-major axis and the semi-minor axis. Multiplying both by pi gives the area.