Competitive Exams

IIT JEE, NEET, ESE, GATE, AE/JE, Olympiad

Only IAS

UPSC, State PSC

School Preparation

Foundation (Class 6-12), Commerce, Arts, CuriousJr (1st - 8th), Science, International Boards

Govt Exam

Judiciary, SSC, Defence, Teaching, JAIIB & CAIIB, BIHAR EXAMS WALLAH, UP Exams, Railway, Nursing Exams, Banking, WB Exams

UG & PG Entrance Exams

MBA, IPMAT, IIT JAM, LAW, CUET UG, UGC NET, GMAT, Design & Architecture, Pharma, CSIR NET, CUET PG, NEET PG

FINANCE

CA, CS, Finance Courses, ACCA

Others

English Wallah, Online Degrees

English Proficiency Test

IELTS, TOEFL

Agriculture

Diameter of a Circle Definition, Formulas, and Steps

Diameter of a circle is the longest straight line passing through the center, touching two points on the circumference. Learn how to calculate it with formulas.

Shruti Dutta16 Dec, 2024

The diameter of a circle is one of its most fundamental measurements. It is defined as the longest straight line that passes through the center of the circle, touching two points on its circumference.

Essentially, the diameter divides the circle into two equal halves. It is always twice the length of the radius, which is the distance from the center to any point on the circumference. The diameter of a circle plays a crucial role in various calculations involving circles, such as determining the circumference and area. Understanding the diameter is key to working with and solving problems related to circles in geometry and real-world applications.

Also Check: Pie Chart

What is Diameter of a Circle?

The diameter of a circle is a line segment that passes through the center, with its endpoints lying on the circumference. In simpler terms, the diameter is the longest chord of the circle. The radius is the distance from the center to any point on the circle, and since the diameter is formed by two radii, it is twice the length of the radius. [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]

Diameter Symbol

Diameter of a Circle: Definition, Symbol, Formula, and Examples

The symbol for diameter is typically represented by the letter "d" . It is often used in mathematical equations and geometric descriptions involving circles. For example, the formula for the diameter of a circle using the radius is:

d=2rd = 2rd=2r

Where:

d is the diameter
r is the radius of the circle

In some cases, the diameter of a circle may also be represented as "2r" to show its direct relationship with the radius.

Also Check: Ordinal Numbers

Diameter of Circle Formula

What is the difference between the diameter and the circumference of a circle? - Quora

The diameter of a circle is a key component that helps define its size. Before diving into the formula for the diameter, let's first understand a few important terms.

The radius (r) is the distance from the center of the circle to any point on its boundary.
The circumference (C) represents the perimeter or the boundary line of the circle.
The area of a circle is the total space enclosed within its boundary. It is calculated using the formula πr², where 'r' stands for the radius.

Steps for the Diameter of a Circle

Step 1 : Identify the radius (r) of the circle. Step 2 : Multiply the radius by 2. Formula : Diameter=2×Radius Example : If the radius is 5 cm, then: Diameter = 2×5 = 10 cm

Steps to Find the Diameter Using the Circumference

Step 1 : Identify the circumference (C) of the circle. Step 2: Divide the circumference by π (approximately 3.14159). Formula : Diameter=Circumference 𝜋 Example : If the circumference is 31.4 cm, then: Diameter=31.4𝜋=31.43.14159≈10cm

Finding the Diameter Using the Area

Step 1 : Identify the area (A) of the circle. Step 2 : Use the area formula Area=𝜋𝑟2, to find the radius first. Rearrange the formula to solve for radius (r): 𝑟=𝐴𝜋 Step 3 : Once you have the radius, multiply it by 2 to find the diameter. Formula : Diameter=2×𝐴𝜋 Example : If the area is 78.5 cm², then: 𝑟=78.5𝜋≈5cm Diameter=2×5=10

Also Check: Trapezium

Diameter of a Circle Using Radius

The diameter of a circle is simply twice the length of the radius. This is because the radius is the distance from the center of the circle to any point on its boundary, and the diameter is the distance across the circle, passing through the center. The formula to find the diameter (d) when the radius (r) is known is: Diameter=2×Radius Example : If the radius of a circle is 5 cm, then the diameter will be: 𝑑=2×5=10cm

Diameter of a Circle Using Circumference

The circumference of a circle is the distance around the circle, or the perimeter. If you know the circumference (C) of the circle, you can calculate the diameter using the relationship between the two. The formula to find the diameter when the circumference is given is: Diameter=Circumference𝜋 Where π (pi) is approximately 3.14159. Example : If the circumference of a circle is 31.4 cm, you can find the diameter by dividing the circumference by π: 𝑑=31.4𝜋≈31.4/3.14159≈10cm This tells you that the diameter is 10 cm.

Diameter Formula Using Area of a Circle:

If you are given the area (A) of a circle, you can calculate the radius first and then find the diameter. The formula for the area of a circle is:

Area=𝜋𝑟2

Where r is the radius. To find the radius from the area, rearrange the formula to solve for r: 𝑟=Area𝜋 Once you have the radius, the diameter is simply twice the radius: Diameter=2×𝑟 Example : If the area of the circle is 78.5 cm², you can first find the radius by using the formula:𝑟=78.5 𝜋=78.5/3.14159≈5cm Now, using the radius, calculate the diameter: 𝑑=2×5=10 cm So, the diameter of the circle is 10 cm.

Also Check: Perimeter of a Triangle

[video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Curious-Jr-Ad.mp4"][/video]

The Relationship Between Radius and Diameter

The radius and diameter are two fundamental measurements that define the size of a circle. They are directly related to each other, and understanding their relationship is crucial when working with various circle-related calculations. The diameter is always twice the length of the radius, while the radius is half of the diameter. Below is a table that highlights the key differences and relationships between the radius and diameter to help you better understand these concepts.

Aspect	Diameter	Radius
Definition	The diameter is a straight line that passes through the center of the circle and touches two points on the circumference.	The radius is the distance from the center of the circle to any point on its circumference.
Relationship	The diameter is twice the length of the radius.	The radius is half the length of the diameter.
Formula	d=2rd = 2rd=2r (Diameter = 2 × Radius)	r=d2r ={d}{2}r=2d (Radius = Diameter ÷ 2)
Length Comparison	The diameter is always greater than the radius.	The radius is always smaller than the diameter.
Position	The diameter extends from one side of the circle to the other, passing through the center.	The radius extends from the center of the circle to any point on the edge (circumference).
Size	The diameter is the longest chord of the circle, and it cuts the circle into two equal halves.	The radius is the shorter line compared to the diameter.
Relation to Circumference	The diameter is directly used in the formula for calculating the circumference: C=πdC = \pi dC=πd.	The radius is used in the circumference formula as well: C=2πrC = 2\pi rC=2πr.
Relation to Area	The diameter is not directly used in the area formula, but it is related because r=d2r = \frac{d}{2}r=2d.	The radius is used in the area formula: A=πr2A = \pi r^2A=πr2.
Measurement Example	If the diameter of a circle is 10 cm, then the radius is 102=5 cm\frac{10}{2} = 5 \, \{cm}210=5cm.	If the radius of a circle is 5 cm, then the diameter is 2×5=10 cm2 \times 5 = 10\,{cm}2×5=10cm.

Related Articles
Subtraction Sums	Word Problems
What is an Abacus?	Math Puzzles
Multiplication Worksheets :	Multiplication Sums

Diameter of a circle FAQs

What is the diameter of a circle?

The diameter of a circle is the longest straight line that passes through the center of the circle and touches two points on its circumference. It is twice the length of the radius.

How is the diameter related to the radius? The diameter is always twice the length of the radius. In other words, if you know the radius, you can find the diameter by multiplying it by 2. The formula is: 𝑑=2𝑟 Can the diameter be smaller than the radius?

No, the diameter is always larger than the radius. The diameter is exactly twice the length of the radius, so it is always longer.

Why is the diameter important in circle-related calculations?

The diameter plays a crucial role in calculating other important circle measurements, such as the circumference and area. Knowing the diameter allows you to quickly find these measurements using well-established formulas.

Can the diameter be smaller than the radius?

No, the diameter is always larger than the radius. The diameter is exactly twice the length of the radius, so it is always longer.

🔥 Trending Blogs

What are Extracurricular Activities, Types and Benefits

NCERT Solutions for Class 5 Maths Chapter 9 Boxes and Sketches

Mental Maths Questions With Solutions, Download PDF

Natural Phenomena for Class 8 Junior Explorers

Addition Word Problems for Class 3, Download PDF

Talk to a counsellorHave doubts? Our support team will be happy to assist you!

7019243492

07019243492

Check out these Related Articles

CURIOUS JUNIOR

Even Numbers: Definition, Example, Properties, List 1 to 1000

Read Full Story

1 Aug 2025, 01:13 pm

CURIOUS JUNIOR

Separation of Substances: Class 6 Science

Read Full Story

1 Aug 2025, 01:09 pm

CURIOUS JUNIOR

Trapezium: Properties, Types, Formulas, and Applications

Read Full Story

1 Aug 2025, 01:12 pm

CURIOUS JUNIOR

Adjectives - Definition, Types, Forms, Usage, Examples

Read Full Story

1 Aug 2025, 01:08 pm

CURIOUS JUNIOR

List of Homophones Words A to Z

Read Full Story

1 Aug 2025, 01:07 pm

CURIOUS JUNIOR

How to Write 15000 in Words in English, Check Here

Read Full Story

1 Aug 2025, 01:06 pm

CURIOUS JUNIOR

Class 8 Sound: Adventure into the World of Sound

Read Full Story

1 Aug 2025, 01:05 pm

CURIOUS JUNIOR

What are Length, Width, and Height: Key Differences with Examples

Read Full Story

1 Aug 2025, 01:04 pm

CURIOUS JUNIOR

Odd Numbers: Definition, Types, Examples and Properties

Read Full Story

1 Aug 2025, 01:03 pm

Join 15 Million students on the app today!

Live & recorded classes available at ease

Dashboard for progress tracking

Millions of practice questions at your fingertips

Free Learning Resources

PW Books

Notes (Class 10-12)

Class 10 Math's Notes

Class 10 Chemistry Notes

Class 10 Physics Notes

lass 10 Biology Notes

Aptitude & Reasoning

Class 10 Geography

Physics Class 11 Notes

Class 11 Chemistry Notes

Maths Notes Class 11

Zoology Class 11

Class 11 Botany Notes

Physics Class 12 notes

Chemistry Class 12

Maths Notes Class 12

Zoology class 12

Class 12th Botany Notes

PW Study Materials

Arjuna JEE Study Material

JEE 5 PYQs

JEE Mind Maps

Yakeen Study Material

NCERT Punch

Arjuna Neet Study Material

NEET PYQs

CBSE Sample Paper

CBSE Question Bank

Udaan For Class 10th Study Material

Notes (Class 6-9)

Class-6 Theory & Notes

Math's Notes for class 7

Science Notes for class 7

Class 8 Math Notes

Class 8 Chemistry Notes

Class 8 Physics Notes

Class 8 Biology Notes

Class 8 SST Notes

Class 9 Math's Notes

Class 9 Physics Notes

Class 9 Chemistry Notes

Class 9 Biology Notes

Ncert Solutions

NCERT Solutions For Class 6

NCERT Solutions For class 7

NCERT Solutions for class 8

NCERT Solutions for class 9

NCERT Solutions for class 10

NCERT Solutions for class 11

NCERT Solutions for Class 12

NCERT Solutions For Class 6

Govt Exams

Entrance Exams

Our Other Websites

Class 6th to 12th Online Courses

Class 12 Online Course

Class 11 Online Course

Class 10 Online Course

Class 9 Online Course

Class 8 Online Course

Govt Job Exams Courses

SSC Online Coaching

Bank Exam Online Coaching

TET Online Coaching

JAIIB & CAIIB Online Coaching

Bihar Exam Online Coaching

UPSC Coaching

UPSC Online Coaching

UPSC Offline & Hybrid Coaching

State PSC Online Coaching

UPPSC Online Coaching

BPSC Online Coaching

Defence Exam Coaching

NDA Online Coaching

CDS Online Coaching

AFCAT Online Coaching

Agniveer Online Coaching

Gate Exam Coaching

Civil Engineering Courses

Mechanical Engineering Courses

Formulas

Other Exams

Company Secretary Exam

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

Also Check: Pie Chart

What is Diameter of a Circle?

Diameter Symbol

d=2rd = 2rd=2r

Where:

d is the diameter
r is the radius of the circle

In some cases, the diameter of a circle may also be represented as "2r" to show its direct relationship with the radius.

Also Check: Ordinal Numbers

Diameter of Circle Formula

The diameter of a circle is a key component that helps define its size. Before diving into the formula for the diameter, let's first understand a few important terms.

The radius (r) is the distance from the center of the circle to any point on its boundary.
The circumference (C) represents the perimeter or the boundary line of the circle.
The area of a circle is the total space enclosed within its boundary. It is calculated using the formula πr², where 'r' stands for the radius.

Steps for the Diameter of a Circle

Step 1 : Identify the radius (r) of the circle. Step 2 : Multiply the radius by 2. Formula : Diameter=2×Radius Example : If the radius is 5 cm, then: Diameter = 2×5 = 10 cm

Steps to Find the Diameter Using the Circumference

Finding the Diameter Using the Area

Also Check: Trapezium

Diameter of a Circle Using Radius

Diameter of a Circle Using Circumference

Diameter Formula Using Area of a Circle:

If you are given the area (A) of a circle, you can calculate the radius first and then find the diameter. The formula for the area of a circle is:

Area=𝜋𝑟2

Also Check: Perimeter of a Triangle

[video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Curious-Jr-Ad.mp4"][/video]

The Relationship Between Radius and Diameter

Aspect	Diameter	Radius
Definition	The diameter is a straight line that passes through the center of the circle and touches two points on the circumference.	The radius is the distance from the center of the circle to any point on its circumference.
Relationship	The diameter is twice the length of the radius.	The radius is half the length of the diameter.
Formula	d=2rd = 2rd=2r (Diameter = 2 × Radius)	r=d2r ={d}{2}r=2d (Radius = Diameter ÷ 2)
Length Comparison	The diameter is always greater than the radius.	The radius is always smaller than the diameter.
Position	The diameter extends from one side of the circle to the other, passing through the center.	The radius extends from the center of the circle to any point on the edge (circumference).
Size	The diameter is the longest chord of the circle, and it cuts the circle into two equal halves.	The radius is the shorter line compared to the diameter.
Relation to Circumference	The diameter is directly used in the formula for calculating the circumference: C=πdC = \pi dC=πd.	The radius is used in the circumference formula as well: C=2πrC = 2\pi rC=2πr.
Relation to Area	The diameter is not directly used in the area formula, but it is related because r=d2r = \frac{d}{2}r=2d.	The radius is used in the area formula: A=πr2A = \pi r^2A=πr2.
Measurement Example	If the diameter of a circle is 10 cm, then the radius is 102=5 cm\frac{10}{2} = 5 \, \{cm}210=5cm.	If the radius of a circle is 5 cm, then the diameter is 2×5=10 cm2 \times 5 = 10\,{cm}2×5=10cm.

Related Articles
Subtraction Sums	Word Problems
What is an Abacus?	Math Puzzles
Multiplication Worksheets :	Multiplication Sums