Perimeter and Area of Ellipse Calculator

Enter the Radius of Major axis(r1):
Enter the Radius of Minor axis(r2):

Perimeter of Ellipse:
Area of Ellipse:

 

Perimeter and Area of Ellipse Calculator is an online tool that is used to calculate the area and perimeter of an ellipse, provided the radius of the major axis and minor axis are given. BYJU’S calculator is available for free here so that students can make ample use of it, to solve mathematical problems. Sometimes even after using the right formulas, we are not sure about the answers. Therefore, we can use the calculator to check the accuracy of the answer.

This calculator here is very easy to use, where we need to enter the known values in the input field to get the result. Before we move ahead to understand how to use ellipse calculator here, let us first understand what is area and perimeter of ellipse.

Area and Perimeter of Ellipse

Ellipse: A two-dimensional shape, which is the locus of points surrounding the curve and the sum of their distances from two fixed points is constant, is called ellipse. The two fixed points here are called foci. Ellipse looks like an oval shape.

Area of Ellipse: The area of the ellipse is the region covered by an ellipse in a two-dimensional plane. If r1 and r2 are the length of the major axis and minor axis of an ellipse, respectively, then the formula of the area is given by:

Area = πr1r2

Perimeter of Ellipse: The distance covered by the outer boundary of an ellipse to complete one cycle, is called perimeter.

\(\text {Perimeter}=2 \pi \sqrt{\frac{r_{1}^{2}+r_{2}^{2}}{2}}\)

How to use Perimeter and Area of Ellipse Calculator?

To find area and perimeter of ellipse using calculator, follow the below given steps:

Step 1: Mention the value of major axis and minor axis of ellipse in the respective fields.

Step 2: Click the “Calculate” button to get the result

Step 3: The area and perimeter with respect to major and minor axis will appear in the respective output fields.

Example

Find the area and perimeter of an ellipse whose semi-major axis is 10 cm and semi-minor axis is 5 cm.

Solution:

Major axis = 10 cm

Minor axis = 5cm

Area = πr1r

A = π x 10 x 5 = 157 sq.cm.

\(\text {Perimeter}=2 \pi \sqrt{\frac{r_{1}^{2}+r_{2}^{2}}{2}}\) \(\begin{array}{l} =2 \pi \sqrt{\frac{10^{2}+5^{2}}{2} \mathrm{cm}} \\ =2 \pi \sqrt{\frac{100+25}{2} \mathrm{cm}} \\ =2 \times 3.14 \times 7.91 \mathrm{cm} \\ =49.674 \mathrm{cm} \end{array}\)

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