Area of an Ellipse Calculator
Calculate the area of an ellipse using A = π×a×b where a and b are the semi-major and semi-minor axes. Also find circumference, eccentricity, and focal distance.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Area of an Ellipse Calculator | — | A = π × a × b | square units |
Step-by-Step Examples
a=5, b=3.
- A=π×5×3=15π≈47.12
- e=√(1−9/25)=√0.64=0.8
- c=√(25−9)=4
a=b=4 (circle).
- A=π×4×4=16π≈50.27
- e=0 (circle has zero eccentricity)
- Becomes A=πr²
Earth orbit: a=149.6M km, b=149.58M km.
- A=π×149.6×149.58≈70,284 M km²
- Nearly circular: e≈0.017
Real-World Applications
Common Mistakes to Avoid
a and b are SEMI-axes (half the diameter). If you measure the full lengths, divide by 2.
a is the semi-major (longer) axis, b the semi-minor (shorter). If b > a, swap them.
There is no simple exact formula for ellipse circumference. The approximation π√(2(a²+b²)) is commonly used.
Frequently Asked Questions
Related Math Calculators
Formula Explorer connections
Interpretation: This relationship connects dimensions, coordinates, angles or trigonometric ratios to a geometric measurement. Assumption: Use a consistent angle mode and length unit, identify the intended shape or coordinate system, and verify that the supplied dimensions form valid geometry.