Area of Ellipse
2026-02-28 11:35 Diff
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Last updated on September 15, 2025

Area is the space inside the boundaries of a two-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of the ellipse.

What is the Area of Ellipse?

An ellipse is a two-dimensional shape that looks like an elongated circle. It has two axes: the major axis, which is the longest diameter, and the minor axis, which is the shortest diameter.

The area of the ellipse is the total space it encloses.

Area of the Ellipse Formula

To find the area of the ellipse, we use the formula: π × a × b, where a and b are the semi-major and semi-minor axes, respectively.

Derivation of the formula:- An ellipse is essentially a stretched circle, and its area can be thought of as a scaled version of a circle's area. The area of a circle is πr². For an ellipse, the radius is replaced by the semi-major and semi-minor axes. Therefore, the area of the ellipse = π × a × b

How to Find the Area of Ellipse?

We can find the area of the ellipse using the formula where the semi-major and semi-minor axes are commonly used. The area of the ellipse is calculated as follows:

Method Using the Semi-Major and Semi-Minor Axes

If the semi-major axis a and the semi-minor axis b are given, we find the area of the ellipse using the formula: Area = π × a × b

For example, if a and b are 5 cm and 3 cm, respectively, what will be the area of the ellipse? Area = π × a × b = π × 5 × 3 = 15π The area of the ellipse is 15π cm²

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Unit of Area of Ellipse

We measure the area of an ellipse in square units. The measurement depends on the system used:

In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²)

In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²)

Special Cases or Variations for the Area of Ellipse

There are no special formulas for the area of an ellipse since it is calculated using the semi-major and semi-minor axes. However, understanding the orientation and the axes can be critical:

Case 1: Circular Shape If the ellipse becomes a circle (a = b), the area is calculated using the formula for a circle, Area = πr², where r is the radius.

Case 2: Rotated Ellipse If the ellipse is rotated but the axes are given, use the formula Area = π × a × b for the calculation.

Tips and Tricks for Area of Ellipse

To ensure that you get correct results while calculating the area of the ellipse, here are some tips and tricks you should know about:

  • The semi-major and semi-minor axes are distinct and should not be confused.
     
  • Ensure you use the correct units when calculating the area, and convert if necessary to maintain consistency. π is approximately 3.14159, but using a calculator with a π function is more precise.

Common Mistakes and How to Avoid Them in Area of Ellipse

It is common for students to make mistakes while finding the area of the ellipse. Let’s take a look at some mistakes made by students.

Problem 1

The semi-major axis a and semi-minor axis b of an elliptical garden are given as 7 m and 4 m. What will be the area?

Okay, lets begin

We will find the area as 28π m²

Explanation

Here, the semi-major axis a is 7 m and the semi-minor axis b is 4 m.

The area of the ellipse = π × a × b = π × 7 × 4 = 28π m²

Well explained 👍

Problem 2

What will be the area of the ellipse if the semi-major axis is 8 cm and the semi-minor axis is 5 cm?

Okay, lets begin

We will find the area as 40π cm²

Explanation

If the semi-major and semi-minor axes are given, we use the formula, area of the ellipse = π × a × b.

Here, a and b are 8 cm and 5 cm.

Hence, the area will be π × 8 × 5 = 40π cm²

Well explained 👍

Problem 3

The area of the ellipse is 36π m² and the length of the semi-major axis a is 6 m.

Okay, lets begin

We find the length of the semi-minor axis b as 6 m

Explanation

To find the semi-minor axis, use the formula area = π × a × b.

Here, the area of the ellipse is given as 36π m², and the length of semi-major axis a is 6 m.

Substitute the values: 36π = π × 6 × b 36 = 6 × b b = 36/6 = 6

Well explained 👍

Problem 4

Find the area of the ellipse if its semi-major axis is 10 cm and the semi-minor axis is 7 cm.

Okay, lets begin

We will find the area as 70π cm²

Explanation

The given semi-major axis is 10 cm and the semi-minor axis is 7 cm.

If the axes are given, we find the area of the ellipse using the formula π × a × b.

Substituting the values in the formula: Area = π × 10 × 7 = 70π cm²

Well explained 👍

Problem 5

Help Linda find the area of the ellipse if the semi-major axis is 9 m and the semi-minor axis is 3 m.

Okay, lets begin

We will find the area as 27π m²

Explanation

The semi-major axis is 9 m and the semi-minor axis is 3 m.

We calculate the area using the formula π × a × b.

Hence, we find the area of the ellipse as π × 9 × 3 = 27π m²

Well explained 👍

FAQs on Area of Ellipse

1.Is it possible for the area of the ellipse to be negative?

No, the area of the ellipse can never be negative. The area of any shape will always be positive.

2.How to find the area of an ellipse if the lengths of the axes are given?

If the semi-major and semi-minor axes are given, then we find the area using the formula, area = π × a × b

3.How to find the area of an ellipse if only the diameter is given?

If only the diameter is given, divide it by 2 to find the semi-major or semi-minor axis, and then use the formula area = π × a × b.

4.How is the circumference of the ellipse calculated?

The circumference of an ellipse does not have a simple formula like a circle. However, an approximate formula is C ≈ π × [3(a+b) - sqrt((3a+b)(a+3b))].

5.What is meant by the area of the ellipse?

The area of the ellipse is the total space occupied by the ellipse.

Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

Fun Fact

: She has songs for each table which helps her to remember the tables