In summary: Ellipse area = π × a × b, where a and b are the semi-axes. With a = 5 and b = 3, area = π × 5 × 3 ≈ 47.12 square units.
How to find the area of an ellipse
An ellipse's area is pi times the two semi-axes: A = π × a × b, where a is the semi-major axis and b is the semi-minor axis (each measured from the centre). For a = 5 and b = 3, A = π × 15 = about 47.12 square units. When both semi-axes are equal the ellipse is a circle, and the formula collapses into the one used by the area of a circle calculator.
How to use this calculator
Enter the two semi-axes — half the full width and half the full height. If you have the full axis lengths, halve them first. When a equals b, the ellipse is a circle and the formula reduces to π × r².
- Full axes instead of semi-axes is the classic mistake — it quadruples the area, since both numbers double.
- Order does not matter. π × 5 × 3 and π × 3 × 5 give the same answer, so it is fine if you label the axes the other way round.
- Units come out squared: axes in cm give cm².
Ellipse vs circle
A circle is just an ellipse with equal axes, so its area collapses to π × r². For a true circle use the semicircle area calculator for halves, or the sector area calculator for wedge portions.
Frequently asked questions
- What is the formula for the area of an ellipse?
- A = π × a × b, where a and b are the semi-major and semi-minor axes measured from the centre.
- What is the area of an ellipse with axes 5 and 3?
- About 47.12 square units (π × 5 × 3).
- Do I use the full axis or the semi-axis?
- Use the semi-axes (half of each full axis). If you have full lengths, divide each by 2 first.
- What happens when a equals b?
- The ellipse becomes a circle and the area equals π × r².
- Can I use the same formula for the perimeter of an ellipse?
- No — an ellipse's perimeter has no simple exact formula and needs an approximation such as Ramanujan's. Only the area is neat; do not assume the circle's 2πr generalises the way πr² does.