Ellipse Area
Calculator
Results
- Area
- 75.398223
- Perimeter (Ramanujan approximation)
- 31.730875
Results
| Area | 75.398223 |
| Perimeter (Ramanujan approximation) | 31.730875 |
formula-map diagram
- Area
- 75.398223
- Perimeter (Ramanujan approximation)
- 31.730875
Formula map
Formula
A = π × a × b= 75.398223686155
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
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See all →Frequently asked questions
What do the two inputs represent?+
The semi-major axis (a) and semi-minor axis (b) — half the length of the ellipse's longest diameter and half the length of its shortest diameter.
What is the formula for the area?+
Area equals π times a times b (A = πab). It is a direct generalization of the circle's area formula, where a circle is just an ellipse with a = b = r.
Do I enter the full axis lengths or the half-lengths?+
Enter the semi-axes — half the full width and half the full height of the ellipse. Entering the full diameters instead will overstate the area by a factor of 4.
Why doesn't this calculator give the perimeter too?+
Unlike area, the ellipse's perimeter has no simple exact formula — it requires an elliptic integral or a numerical approximation, which is a separate and more complex calculation.
What if a and b are the same value?+
Then the ellipse is actually a circle, and the formula πab reduces to πr², matching the standard circle area formula exactly.