Ellipse Area Calculator
Area is simply π times both semi-axes, but the perimeter has no closed elementary form — this uses Ramanujan’s approximation.
Your numbers
Area
188.5cm²
Circumference
51.05cm
Formula
Area = π × Semi-major axis × Semi-minor axis
Equal semi-axes give a circle. Entering diameters instead of semi-axes quadruples the area.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Semi-major axis (cm)The longer radius of an ellipse. | 10 | 0 and up |
| Semi-minor axis (cm)The shorter radius of an ellipse. | 6 | 0 and up |
Step by step
Quick reference table
Results when only Semi-major axis (cm) changes and everything else stays put.
| Semi-major axis (cm) | Area (cm²) | Circumference (cm) |
|---|---|---|
| 5 | 94.25 | 34.63 |
| 7.5 | 141.37 | 42.54 |
| 10 | 188.5 | 51.05 |
| 15 | 282.74 | 69.04 |
| 20 | 376.99 | 87.72 |
What each result means
| Result | At default values |
|---|---|
| Area (cm²)The space a shape covers — length squared. | 188.5 |
| Circumference (cm)The distance once around a circle. | 51.05 |
Common mistakes
Equal semi-axes give a circle. Entering diameters instead of semi-axes quadruples the area.
Glossary
- Semi-major axis
- The longer radius of an ellipse.
- Semi-minor axis
- The shorter radius of an ellipse.
- Area
- The space a shape covers — length squared.
- Circumference
- The distance once around a circle.
Frequently asked questions
Q. How is Ellipse Area Calculator calculated?
Area = π × Semi-major axis × Semi-minor axis — Area is simply π times both semi-axes, but the perimeter has no closed elementary form — this uses Ramanujan’s approximation.
Q. Can you walk through an example?
With Semi-major axis 10cm, Semi-minor axis 6cm, the answer is Area 188.5cm².
Q. What do I need to enter?
Enter Semi-major axis, Semi-minor axis. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Semi-major axis (cm) moves the answer to Semi-major axis (cm) 5 → Area (cm²) 94.25 and Semi-major axis (cm) 20 → Area (cm²) 376.99. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Equal semi-axes give a circle. Entering diameters instead of semi-axes quadruples the area.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.