Ellipse area and perimeter calculator
Enter the semi-major and semi-minor axes to get the area and perimeter, handy for oval tables and flower beds.
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How to use it
- Enter semi-major axis a, semi-minor axis b and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Area = π × a × b. The perimeter is computed exactly with the Gauss arithmetic-geometric mean method; eccentricity = √(1 − b² ÷ a²), with a ≥ b.
Example
Inputs: Semi-major axis a = 5, Semi-minor axis b = 3, Length unit = Centimeters (cm). Result: Area: 47.1239 cm²; Perimeter: 25.527 cm; Eccentricity: 0.8.
Limits and caveats
- There is no simple closed formula for the perimeter; it is computed numerically to machine precision.
- Enter semi-axes, not full axes: halve the overall length and width.
Questions about this tool
What is the area formula for an oval?
π times the semi-major axis times the semi-minor axis. A 10 × 6 table has semi-axes 5 and 3 and an area of about 47.12.
Why does the perimeter differ from an approximation I found?
Approximations such as Ramanujan's are very close. This tool computes the exact value, so far decimals may differ.
What does eccentricity mean?
A number from 0 to 1 that measures how stretched the ellipse is: 0 is a circle and values near 1 are very flat.