Ellipse Area Calculator
The area of an ellipse — π times the two semi-axes, with a good approximation of its perimeter.
An ellipse is a circle stretched in one direction, so its area is πab where a and b are the half-widths.
How the ellipse area calculator works
An ellipse is a circle stretched in one direction, so its area is πab where a and b are the half-widths. When a equals b it collapses neatly back to πr². The perimeter is the awkward part: it has no closed form in elementary functions, so this page uses Ramanujan's second approximation, which is accurate to better than one part in ten million for ordinary shapes.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Semi-axes 6 and 4 | 75.3982 | 75.4 |
| A circle in disguise | 78.5398 | 78.54 — the same as πr² |
| A long thin ellipse | 188.4956 | 188.5 |
FAQFrequently asked questions
What is the area of an ellipse?
πab, where a and b are the semi-axes — half the long width and half the short width.
What is a semi-axis?
Half of the full width across that direction, measured from the centre.
Why is the perimeter approximate?
Because it cannot be written with ordinary functions — it needs an elliptic integral. Ramanujan's approximation used here is accurate to about one part in ten million.
Is a circle an ellipse?
Yes, the special case where both axes are equal.
How do I get the area from the full widths?
Halve each first — a 12 by 8 ellipse has semi-axes of 6 and 4.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.