Ellipse Area Calculator

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Ellipse — is a closed curve on a plane that can be obtained as the intersection of a plane and a circular cylinder or as an orthogonal projection of a circle onto a plane.

An ellipse is a closed curve that is symmetrical along its major and minor axis. To find the area of an ellipse, you need to know the length of the major and minor axis. The formula for the area of an ellipse is:

S = \pi * a * b

or

S = \pi * r * R

where:

• S is the area of the ellipse
• a is the length of the major axis
• b is the length of the minor axis
• R is the length of the semi-major axis
• r is the length of the semi-minor axis
• π (pi) is a mathematical constant approximately equal to 3.14159

Our Ellipse Area Calculator makes it easy to find the area of your ellipse. To use the calculator:

1. Enter the length of the minor axis (b) or semi-minor axis (r) in the first box.
2. Enter the length of the major axis (a) or semi-major axis (R) in the second box.
3. Our calculator automaticaly will give you the area of your ellipse.

Here's an example:

Example: If the major axis (a) of an ellipse is 10 units and the minor axis (b) is 6 units, then the area S will be:

S = πab = π x 10 x 6 = 60π ≈ 188.5

So, the area of the ellipse will be approximately 188.5 square units.

Ellipse Area Formulas

There are other formulas that can be used to find the area of an ellipse:

S = \pi * r_1 * r_2

S = \dfrac{1}{2} * a * b*sin(\alpha)

where:

• r₁ and r₂ are the lengths of the semi-major and semi-minor axis
• a and b are the lengths of the major and minor axis
• α is the angle between the major axis and a line through the center of the ellipse and a point on the ellipse

While these formulas are less commonly used, it's important to be aware of them in case you encounter them in your studies.

Conclusion

Calculating the area of an ellipse is an important skill in geometry. Our Ellipse Area Calculator and formula make it easy to find the area of your ellipse. Try it out for yourself and see how easy it can be!