Area of a Circle Definition, Formula, Examples, Real Life Application
Area of a Circle: Learn how to calculate the area using the radius, diameter, or circumference. Explore formulas and real-life applications of this geometric concept.
Shruti Dutta16 Dec, 2024
Share
The area of a circle refers to the total space enclosed within the circle's boundary. It is a measure of how much surface the circle covers.
The area is expressed in square units, such as square meters (m²) or square centimeters (cm²). To calculate the area, the radius (the distance from the center of the circle to any point on its boundary) is typically used. The formula for the area of a circle is simple and involves multiplying the square of the radius by the mathematical constant π (Pi), which is approximately 3.14 or 22/7. The area of a circle is an important concept in geometry and is used in various applications like calculating the size of circular objects, land areas, and more.Also Check: Pie Chart
[video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Copy-of-Corurious-Jr-Reel-2-Landscape-1-2-1.mp4"][/video]What is the Area of a Circle?
The area of a circle refers to the total space enclosed by the circle's boundary. It represents the number of square units that fit inside the circle. The formula to calculate the area of a circle is given by:Area of Circle = πr² or πd²/4,
where:- π (Pi) is approximately 22/7 or 3.14.
- r is the radius of the circle.
- d is the diameter of the circle.
Also Check: Natural Numbers
Area of Circle Formulas
The area of a circle can be calculated using several methods, depending on the available information, such as the radius, diameter, or circumference. While it is possible to calculate the area through intermediate steps by first finding the radius from the diameter or circumference, the following formulas provide the most direct method. For a circle with radius 'r', the area is calculated as:Area of a Circle (A) = πr² square units ,
where:- π (Pi) is approximately 22/7 or 3.14,
- r is the radius of the circle.
Area = (π/4) × d² ,
where d is the diameter of the circle. If the circumference 'C' is known, the area can be calculated using:Area = C² / 4π ,
where C is the circumference of the circle. Additionally, the circumference (or perimeter) of the circle is given by:Circumference = 2πr units .
[video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Curious-Jr-Ad.mp4"][/video] The area of a circle can be calculated using the following formulas:- When the radius is known: A = π r²
- When the diameter is known: A = (π/4) × D²
- When the circumference is known: A = C² / 4π
Example:
What is the area of a circle with a radius of 3 meters? Given: Radius r = 3 meters Using the formula A = π r² , we get: A = π × 3² A = 3.14159... × (3 × 3) A = 28.27 m² (rounded to two decimal places)Area of a Circle Using Diameter
The area of a circle can also be calculated directly using its diameter . The formula is: Area of a Circle = πd² / 4 , where d is the diameter of the circle. Since the diameter is twice the radius (d = 2r), traditionally, we would first find the radius from the diameter and then calculate the area. However, this formula allows us to directly find the area from the diameter itself, making the process simpler.Area of a Circle Using Circumference
You can also find the area of a circle using its circumference. The formula for this is: Area of a Circle = C² / 4π , where C is the circumference of the circle. Typically, we would first calculate the radius from the circumference and then use it to find the area. However, with this formula, we can directly compute the area from the circumference, making it more efficient.Also Check: Pie Chart
Surface Area of a Circle Formula
The term surface area of a circle is the same as its area. When we refer to the area of a circle, we are essentially talking about its total surface area. However, in geometry, the term "surface area" is typically used for three-dimensional objects, such as spheres, where it refers to the area covering the surface. Since a circle is a two-dimensional shape, we simply call it the " area " of the circle, not the surface area. [video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Courios-jr-Video.mp4"][/video] To calculate the area (or surface area) of a circle, you can use the following formula: Area (Surface Area) of a Circle = πr² , where:- r is the radius of the circle.
- π (Pi) is approximately 3.14 or 22/7.
Also Check: Even Numbers
Real-Life Applications of the Area of a Circle
The concept of the area of a circle is widely used in various real-life situations.- Gardens and Landscaping : When designing a circular garden, calculating the area helps determine how much soil, mulch, or grass is needed to cover the space effectively.
- Sports : In sports like cycling or athletics, the area of circular tracks or fields is calculated to estimate capacity, plan layouts, and design the space for optimal use.
- Art and Design : Artists working with circular shapes need to understand the area to plan and scale their projects accurately, whether they are designing round tables, circular paintings, or other objects.
| Related Articles | |
| Subtraction Sums | Word Problems |
| What is an Abacus? | Math Puzzles |
| Multiplication Worksheets: | Multiplication Sums |
Area of a Circle FAQs
What is the area of a circle?
The area of a circle refers to the total space enclosed within the circle's boundary. It is calculated by squaring the radius and multiplying it by Pi (π). The formula is:
Area = πr², where r is the radius of the circle.
What units are used when calculating the area of a circle?
The area of a circle is always expressed in square units. For example, if the radius is given in meters, the area will be in square meters (m²). Similarly, if the radius is in centimeters, the area will be in square centimeters (cm²).
Why is Pi (π) used in the area formula?
Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is essential for calculating the area and other properties of a circle because it relates to the circular shape and its proportions.
Can I use approximations for Pi?
Yes, Pi (π) is often approximated as 3.14 or 22/7, depending on the level of precision needed for your calculation. For most basic calculations, 3.14 is sufficient.
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
Join 15 Million students on the app today!
Live & recorded classes available at easeDashboard for progress trackingMillions of practice questions at your fingertips
Free Learning Resources
PW Books
Notes (Class 10-12)
PW Study Materials
Notes (Class 6-9)
Ncert Solutions
Govt Exams
Class 6th to 12th Online Courses
Govt Job Exams Courses
UPSC Coaching
Defence Exam Coaching
Gate Exam Coaching
Other Exams
Know about Physics Wallah
Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Copyright © 2025 Physicswallah Limited All rights reserved.
