Perimeter of Oval
2026-02-28 10:14 Diff
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Last updated on August 5, 2025

The perimeter of a shape is the total length of its boundary. Calculating the perimeter of an oval, also known as an ellipse, is more complex than for a simple polygon. The perimeter is used in various applications like construction, design, and more. In this topic, we will learn about the perimeter of an oval.

What is the Perimeter of an Oval?

The perimeter of an oval, also called an ellipse, is the total length around its boundary. Unlike simple shapes, calculating the perimeter of an oval requires a more complex approach, as there is no exact formula like for polygons. However, an approximation formula for the perimeter of an oval is given by Ramanujan’s first approximation: 𝑷 ≈ π * [3(a+b) - √((3a + b) * (a + 3b))], where a and b are the semi-major and semi-minor axes of the oval, respectively. For example, if an oval has a semi-major axis a = 6 and a semi-minor axis b = 4, then its approximate perimeter is 𝑷 ≈ π * [3(6+4) - √((3*6 + 4) * (6 + 3*4))].

Formula for Perimeter of Oval - 𝑷 ≈ π * [3(a+b) - √((3a + b) * (a + 3b))].

Let’s consider another example of an oval with semi-major and semi-minor axes, 𝑎 = 8, 𝑏 = 6. So the approximate perimeter of the oval will be: 𝑷 ≈ π * [3(8+6) - √((3*8 + 6) * (8 + 3*6))].

How to Calculate the Perimeter of an Oval

To find the perimeter of an oval, apply the approximation formula by Ramanujan and use the given lengths of the semi-major and semi-minor axes. For instance, a given oval has semi-major axis a = 7 and semi-minor axis b = 5. Perimeter ≈ π * [3(7+5) - √((3*7 + 5) * (7 + 3*5))]. Example Problem on Perimeter of Oval - For finding the approximate perimeter of an oval, we use the formula, 𝑷 ≈ π * [3(a+b) - √((3a + b) * (a + 3b))]. For example, let’s say, a semi-major axis a = 9 cm, and a semi-minor axis b = 6 cm. Now, the approximate perimeter ≈ π * [3(9+6) - √((3*9 + 6) * (9 + 3*6))].

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Tips and Tricks for Perimeter of Oval

Learning some tips and tricks makes it easier to calculate the perimeter of ovals. Here are some tips and tricks given below: Always remember that the perimeter of an oval requires more complex calculations than simple polygons. Use the approximation formula, 𝑷 ≈ π * [3(a+b) - √((3a + b) * (a + 3b))]. When calculating the perimeter of an oval, ensure that you identify the correct lengths for the semi-major and semi-minor axes. This can be done by measuring the longest and shortest diameters of the oval and halving them. To reduce confusion, arrange your calculations systematically and verify your steps when determining the perimeter of a group of ovals. To avoid mistakes when calculating the perimeter, ensure the semi-major and semi-minor axes are precise and constant for practical uses like design and architecture. If you are given an estimated perimeter, verify the calculation by comparing it with different approximation methods or numerical integration techniques for more accuracy.

Common Mistakes and How to Avoid Them in Perimeter of Oval

Did you know that while working with the perimeter of an oval, people might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:

Problem 1

An elliptical racetrack has a semi-major axis of 50 meters and a semi-minor axis of 30 meters. Find the approximate perimeter using Ramanujan's formula.

Okay, lets begin

Approximate perimeter = 252.15 meters.

Explanation

Let a = 50 meters and b = 30 meters. Using Ramanujan’s approximation: 𝑷 ≈ π * [3(50+30) - √((3*50 + 30) * (50 + 3*30))] 𝑷 ≈ π * [3(80) - √((150 + 30) * (50 + 90))] 𝑷 ≈ π * [240 - √(180 * 140)] 𝑷 ≈ π * [240 - √25200] 𝑷 ≈ π * [240 - 158.74] 𝑷 ≈ π * 81.26 𝑷 ≈ 255.15 meters. Therefore, the approximate perimeter is 255.15 meters.

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Problem 2

A garden in the shape of an oval has a semi-major axis of 15 meters and a semi-minor axis of 10 meters. Calculate the approximate perimeter.

Okay, lets begin

Approximate perimeter = 79.07 meters.

Explanation

Given a = 15 meters and b = 10 meters. Using Ramanujan’s approximation: 𝑷 ≈ π * [3(15+10) - √((3*15 + 10) * (15 + 3*10))] 𝑷 ≈ π * [3(25) - √((45 + 10) * (15 + 30))] 𝑷 ≈ π * [75 - √(55 * 45)] 𝑷 ≈ π * [75 - √2475] 𝑷 ≈ π * [75 - 49.75] 𝑷 ≈ π * 25.25 𝑷 ≈ 79.35 meters. Therefore, the approximate perimeter is 79.35 meters.

Well explained 👍

Problem 3

Find the approximate perimeter of an oval with semi-major axis 20 cm and semi-minor axis 14 cm.

Okay, lets begin

Approximate perimeter = 107.06 cm.

Explanation

Using Ramanujan’s approximation: 𝑷 ≈ π * [3(20+14) - √((3*20 + 14) * (20 + 3*14))] 𝑷 ≈ π * [3(34) - √((60 + 14) * (20 + 42))] 𝑷 ≈ π * [102 - √(74 * 62)] 𝑷 ≈ π * [102 - √4588] 𝑷 ≈ π * [102 - 67.73] 𝑷 ≈ π * 34.27 𝑷 ≈ 107.67 cm. Therefore, the approximate perimeter is 107.67 cm.

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Problem 4

An art piece is in the shape of an oval with a semi-major axis of 25 inches and a semi-minor axis of 18 inches. How much material is needed to frame the piece?

Okay, lets begin

Approximate perimeter = 135.47 inches.

Explanation

Using Ramanujan’s approximation: 𝑷 ≈ π * [3(25+18) - √((3*25 + 18) * (25 + 3*18))] 𝑷 ≈ π * [3(43) - √((75 + 18) * (25 + 54))] 𝑷 ≈ π * [129 - √(93 * 79)] 𝑷 ≈ π * [129 - √7347] 𝑷 ≈ π * [129 - 85.72] 𝑷 ≈ π * 43.28 𝑷 ≈ 136.05 inches. Therefore, the approximate perimeter is 136.05 inches.

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Problem 5

An oval mirror has a semi-major axis of 12 cm and a semi-minor axis of 8 cm. Calculate the approximate length around the mirror’s edge.

Okay, lets begin

Approximate perimeter = 63.58 cm.

Explanation

Using Ramanujan’s approximation: 𝑷 ≈ π * [3(12+8) - √((3*12 + 8) * (12 + 3*8))] 𝑷 ≈ π * [3(20) - √((36 + 8) * (12 + 24))] 𝑷 ≈ π * [60 - √(44 * 36)] 𝑷 ≈ π * [60 - √1584] 𝑷 ≈ π * [60 - 39.8] 𝑷 ≈ π * 20.2 𝑷 ≈ 63.45 cm. Therefore, the approximate perimeter is 63.45 cm.

Well explained 👍

FAQs on Perimeter of Oval

1.Evaluate the oval’s perimeter if its semi-major axis is 10 cm and semi-minor axis is 5 cm.

Using Ramanujan’s approximation: 𝑷 ≈ π * [3(10+5) - √((3*10 + 5) * (10 + 3*5))] 𝑷 ≈ π * [45 - √((35) * (25))] 𝑷 ≈ π * [45 - √875] 𝑷 ≈ π * [45 - 29.58] 𝑷 ≈ π * 15.42 𝑷 ≈ 48.43 cm.

2.What is meant by an oval’s perimeter?

The total length around an oval’s boundary is its perimeter. An oval, or ellipse, requires specific methods for this calculation due to its curved shape.

3.What are the axes of an oval?

An oval has two axes: the semi-major axis, which is the longest radius, and the semi-minor axis, which is the shortest radius.

4.Which shape is an oval similar to but not the same as?

An oval is similar to a circle but differs as a circle has all radii equal, while an oval has varying radii.

5.Can a perfect formula be used for the perimeter of an oval?

No, there is no perfect formula for the perimeter of an oval. Approximations like Ramanujan’s formula are commonly used for practical purposes.

Important Glossaries for Perimeter of Oval

Perimeter: The total length of the boundary of a shape. Oval: A curved shape resembling an elongated circle, also known as an ellipse. Semi-major axis: The longest radius of an oval. Semi-minor axis: The shortest radius of an oval. Ramanujan’s approximation: A formula used to estimate the perimeter of an oval.

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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.

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