Key takeaways
- The area of an ellipse is A = π × a × b.
- a and b are half the longest and shortest widths across the ellipse.
- A circle is a special ellipse where a and b are equal.
- Both axes must be halved before multiplying, not used at full length.
In this guide
What is an ellipse?
An ellipse is an oval shape, like a stretched circle. Instead of one radius, it has two: the semi-major axis (the longer half-width) and the semi-minor axis (the shorter half-width).
Why does the area of an ellipse matter?
Ellipses show up in oval rugs, sports fields, and picture frame mats, and their area follows almost the same rule as a circle.
If a and b happen to be equal — say both are 6 m — an ellipse becomes a true circle, andA = π × 6 × 6 = 113.10 m²is exactly the same answer you'd get from a circle of radius 6 m usingπr².
The formula
| Symbol | What it means | Example |
|---|---|---|
| A | The area you want to find | 75.4 m² |
| π (pi) | A fixed number, about 3.14159 | 3.14159 |
| a | The semi-major axis: half the longest diameter | 6 m |
| b | The semi-minor axis: half the shortest diameter | 4 m |
How to find the area step by step
- 1Measure the longest distance across the ellipse (the major axis), then divide by 2 to get a.
- 2Measure the shortest distance across the ellipse (the minor axis), then divide by 2 to get b.
- 3Multiply a by b.
- 4Multiply the result by π.
Now try it yourself. Change a and b in the calculator below and watch the area update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Mixing up which axis is longer. It doesn't actually matter for the formula, since
a × bgives the same result asb × a, but make sure both are halved correctly. - Treating it like a circle with one radius. A circle is a special ellipse where a and b are equal; using a single radius for a true oval gives the wrong area. See the area of a circle calculator for true circles.
- Forgetting square units. Area is always in units², like m² or ft².
Tips and tricks
- To estimate quickly, use 3 for π instead of 3.14159; it's within about 5% of the exact answer.
- For the perimeter (distance around) an ellipse, note there's no simple exact formula like there is for a circle — it needs an approximation.
Where you'll use it in real life
- Home decor: sizing an oval rug or tablecloth.
- Sports: estimating the playing surface of an oval sports field.
- Framing: working out material for an oval picture frame mat.
- Landscaping: calculating the surface area of an oval garden pond.
Quick summary
To find the area of an ellipse, halve the longest and shortest widths to get a and b, multiply them together, then multiply by π. When a and b are equal, the formula becomes a circle's area formula. Use the calculator above to check your own ellipse instantly.
Worked example
You're digging an oval garden pond. The pond is 12 meters long and 8 meters wide at its widest points, giving a semi-major axis of 6 meters and a semi-minor axis of 4 meters. How much surface area will the pond cover?
- 01A = πab
- 02A = π(6)(4)
- 03A = 24π
- 04A = 75.4 m²
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find a and b from an ellipse's full length and width?
Divide both the full length and the full width by 2. The half of the longer measurement is a, and the half of the shorter measurement is b.
What's the difference between a circle and an ellipse?
A circle is a special ellipse where both axes (a and b) are equal, using a single radius. An ellipse is stretched, with a longer axis and a shorter one. See the [area of a circle calculator](/calculator/area-circle) when a and b are the same.
Does it matter which axis I call a and which I call b?
No, since multiplication doesn't depend on order, a × b gives the same area as b × a.
What units is ellipse area measured in?
Square units matching your axis measurements, such as ft² if a and b are measured in feet.
