PRO Courses Hot Guides Tech Help Pro Expert Videos About wikiHow Pro Upgrade
QUIZZES All Quizzes Hot Love Quizzes Personality Quizzes Trivia Quizzes Taylor Swift Quizzes
EDIT Edit this Article
EXPLORE Tech Help ProAbout UsRandom ArticleQuizzes Request a New ArticleCommunity DashboardTrendingForums Arts and EntertainmentArtworkBooksMoviesComputers and ElectronicsComputersPhone SkillsTechnology HacksHealthMen's HealthMental HealthWomen's HealthRelationshipsDatingLoveRelationship Issues Hobbies and CraftsCraftsDrawingGamesEducation & CommunicationCommunication SkillsPersonal DevelopmentStudyingPersonal Care and StyleFashionHair CarePersonal Hygiene Quizzes Love Quizzes Personality Quizzes Fun Games ForumsArts and EntertainmentFinance and BusinessHome and Garden Relationship QuizzesCars & Other VehiclesFood and EntertainingPersonal Care and Style Sports and FitnessComputers and ElectronicsHealthPets and Animals TravelEducation & CommunicationHobbies and CraftsPhilosophy and Religion Work WorldFamily LifeHolidays and TraditionsRelationships Youth
LOG IN
Log in
Social login does not work in incognito and private browsers. Please log in with your username or email to continue. FacebookGooglewikiHow Account No account yet? Create an account
RANDOM
Home
Random
Browse Articles
TrendingNew
Quizzes & Games
All QuizzesHot
Love Quizzes
Personality Quizzes
Fun Games
Dating Simulator
Learn Something New
Forums
Courses
Happiness Hub
Explore More
Support wikiHow
About wikiHow
Log in / Sign up
Terms of Use wikiHow is where trusted research and expert knowledge come together. Learn why people trust wikiHow
Categories
Education and Communications
Studying
Mathematics
Trigonometry
How to Convert Degrees to Radians Download ArticleExplore this Article Steps Steps Other Sections Questions & Answers VideoWATCH NOW Related Articles Expert Interview References Article Summary Co-authored by Joseph Quinones
Last Updated: October 9, 2024 Fact Checked
Download Article ARTICLE VIDEO X
This article was co-authored by Joseph Quinones. Joseph Quinones is a Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,152,359 times.
Degrees and radians are two units for measuring angles. A circle contains 360 degrees, which is the equivalent of 2π radians, so 360° and 2π radians represent the numerical values for going "once around" a circle.[1]XResearch source Sound confusing? Don't worry, you can easily convert degrees to radians, or from radians to degrees, in just a few easy steps.
Practice Problems
Convert Degrees to Radians Practice ProblemsConvert Degrees to Radians Practice Problems ANSWER KEY
Steps
Download Article
1 Write down the number of degrees you want to convert to radians.[2]XResearch source Let's work with a few examples so you really get the concept down. Here are the examples you'll be working with:
Example 1: 120°
Example 2: 30°
Example 3: 225°
2 Multiply the number of degrees by π/180.[3]X Expert Source Joseph QuinonesPhysics TeacherExpert Interview To understand why you have to do this, you should know that 180 degrees constitute π radians. Therefore, 1 degree is equivalent to (π/180) radians. Since you know this, all you have to do is multiply the number of degrees you're working with by π/180 to convert it to radian terms. You can remove the degree sign since your answer will be in radians anyway. Here's how to set it up:[4]XResearch source
Example 1: 120 x π/180
Example 2: 30 x π/180
Example 3: 225 x π/180
Advertisement
3 Do the math. Simply carry out the multiplication process, by multiplying the number of degrees by π/180. Think of it like multiplying two fractions: the first fraction has the number of degrees in the numerator and "1" in the denominator, and the second fraction has π in the numerator and 180 in the denominator. Here's how you do the math:[5]XResearch source
Example 1: 120 x π/180 = 120π/180
Example 2: 30 x π/180 = 30π/180
Example 3: 225 x π/180 = 225π/180
4 Simplify. Now, you've got to put each fraction in lowest terms to get your final answer. Find the largest number that can evenly divide into the numerator and denominator of each fraction and use it to simplify each fraction. The largest number for the first example is 60; for the second, it's 30, and for the third, it's 45. But you don't have to know that right away; you can just experiment by first trying to divide the numerator and denominator by 5, 2, 3, or whatever works. Here's how you do it:[6]XResearch source
Example 1: 120 x π/180 = 120π/180 ÷ 60/60 = 2/3π radians
Example 2: 30 x π/180 = 30π/180 ÷ 30/30 = π/6 radians
Example 3: 225 x π/180 = 225π/180 ÷ 45/45 = 5/4π radians
5 Write down your answer. To be clear, you can write down what your original angle measure became when converted to radians. Then, you're all done! Here's what you do:[7]XResearch source
Example 1: 120° = 2/3π radians
Example 2: 30° = 1/6π radians
Example 3: 225° = 5/4π radians
Advertisement
Community Q&A
Search Add New Question
Question How do I derive the formula for the conversion of degrees to radians? Anan Shah Community Answer Simply: π=180 or π=180*1 degree and therefore, 1degree= π/180, thus, degree measure= radian measure * π/180. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 64 Helpful 73
Question What is 63 degree 14 min 51 sec in radian form? Donagan Top Answerer First convert the angle to a decimal. There are 60 seconds in a minute, 60 minutes in a degree, and 3600 seconds (60 x 60) in a degree. 14 minutes 51 seconds equals 891 seconds, which is 891/3600 of a degree or .2475 degree. For simplicity, let's call that ¼ of a degree. Therefore, the angle in question is 63¼ degrees. As shown in the above article, 63¼° multiplied by (π/180) = 1.1 radians. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 44 Helpful 83
Question What is 1085 degrees in radian form? Donagan Top Answerer 1085° = 6.0277 radians. 1080° is equivalent to three complete circles, 1085° is the same angle as 5° and 0.0277 radian. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 61 Helpful 39
See more answers Ask a Question 200 characters left Include your email address to get a message when this question is answered. Submit Advertisement
Video
Tips
Submit a Tip All tip submissions are carefully reviewed before being published Name Please provide your name and last initial Submit Thanks for submitting a tip for review!
You Might Also Like
How toConvert Radians to DegreesHow toMemorize the Unit CircleEasy Steps to Find the Reference Angle in Degrees & Radians2 Different Ways to Find a Circle’s Arc Length How to Figure Out the Circumference of a Circle: Easy Math TutorialHow to Find Coterminal AnglesHow to Find the Radius of a CircleHow toCalculate FrequencyHow to Memorize Trigonometric Functions2 Easy Ways to Use a ProtractorHow toCalculate the Area of a SectorHow to Find Direction of a VectorHow toMeasure an Angle Without a ProtractorHow toFind the Circumference and Area of a Circle Advertisement
Expert Interview
Thanks for reading our article! If you’d like to learn more about physics, check out our in-depth interview with Joseph Quinones.
Co-authored by: Joseph Quinones Physics Teacher This article was co-authored by Joseph Quinones. Joseph Quinones is a Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. This article has been viewed 1,152,359 times. 29 votes - 82% Co-authors: 18Updated: October 9, 2024 Views: 1,152,359 Categories: TrigonometryArticle SummaryX
To convert degrees to radians, take the number of degrees to be converted and multiply it by π/180. You can calculate this by converting both numbers into fractions. For example, to convert 120 degrees you would have 120 x π/180 = 120π/180. Once you’ve gotten your answer, simplify the radians. For more examples of converting degrees to radians, scroll down!Did this summary help you?YesNo
In other languages Russian Spanish German French Italian Portuguese Indonesian Dutch Arabic Chinese Vietnamese Korean Thai Turkish Hindi Persian Czech Japanese
Print
Send fan mail to authors
Thanks to all authors for creating a page that has been read 1,152,359 times.
Reader Success Stories
Sidharth Rai
Apr 6, 2018
"This article helped me in my prelims. I'm so thankful to wikiHow. I cannot express in words how much wikiHow has helped these years, just amazing. They work selflessly just to provide knowledge. I've become a big fan of this website."..." more
More reader stories Hide reader stories Share your story
Did this article help you?
Yes No Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Co-authored by: Joseph Quinones Physics Teacher Co-authors: 18Updated: October 9, 2024 Views: 1,152,35982% of readers found this article helpful. 29 votes - 82% Click a star to add your vote
Sidharth Rai
Apr 6, 2018
"This article helped me in my prelims. I'm so thankful to wikiHow. I cannot express in words how much wikiHow has helped these years, just amazing. They work selflessly just to provide knowledge. I've become a big fan of this website."..." more
Shannon Green
Jan 25, 2017
"I was having a major math test tomorrow and had no idea how to convert radians to degrees. I googled it, found this site, and it explained it really well!"..." more
Natalie Tellechea
Apr 15, 2019
"Very well-written, clear, and accurate steps are given here, with a number of examples providing extra support. " Rated this article:
Prudence Makwakwa
Feb 13, 2017
"This article did help me a lot in solving mathematics problems and with conversions. Thanks a lot. "
A. S.
Feb 12, 2024
"This summarized an entire week of Geometry class! The authors simplified everything for me (pun)! ." Rated this article: Share yours! More success stories Hide success stories
Quizzes & Games
How Many Digits of Pi Do I Know QuizTake QuizGreek Alphabet QuizTake QuizHow Much Do I Know About Space QuizTake QuizAm I Smarter than a 5th Grader QuizTake QuizHow Lucky Am I QuizTake QuizIQ Test For KidsTake Quiz
You Might Also Like
How toConvert Radians to DegreesHow toMemorize the Unit CircleEasy Steps to Find the Reference Angle in Degrees & Radians2 Different Ways to Find a Circle’s Arc Length
Featured Articles
What Are the Korean Animal Face Types? (And Which Type Do You Have?)Being the Little Spoon While Cuddling: Is It Better Than the Big Spoon?115+ Funny “Get Well Soon” Messages to Make Someone Laugh110+ “Fun Facts” for Interviews, Introductions, & IcebreakersHow Long Would You Survive In A Zombie Apocalypse?How to Roast Someone in a Rap Battle (Plus the Best Bars of All Time)
Trending Articles
How toMake OutWhat Song Was #1 On My Birthday?How Many People Had a Crush on Me This Year? Find Out HereBest Personality TestDo I Have Common Sense QuizDaily Horoscope (All Signs): What Do The Stars Predict Today?✩⟡˚₊‧
Featured Articles
What Turns a Girl On? 31 Things to Try on Your PartnerLove AnalyzerSending Your Sweetie a Love Note? Here are 200+ Romantic IdeasHow toExercise Your BrainHow toBe a Fun Person to Hang out WithWhat Does Your Morning Routine Say About You?
Featured Articles
How toDevelop Productive HabitsHow toPractice Self CareWhat Song Matches Your Life Right Now?Your 2026 Vision: What Does Next Year Hold?Understanding the Most Attractive Face Shapes (& Determining Your Own)Type A B C D Personality Test
Watch Articles
How to Deep Clean Your Kitchen Sink (& Keep It Clean)How to Curl Your Hair: 8 Easy & Quick WaysHow toThicken Sauce with FlourHow to Brighten Up White Shirts and Other GarmentsHow to Cook White Rice without a Rice CookerHow to Clean Out the Inside of a Glass Bottle (With or Without a Brush)
Trending Articles
Compatibility TestWhat Am I Craving Quiz150 Unique & Sentimental Ways to Say “Happy New Year”30+ New Year’s Eve Games to Keep Your NYE Party GoingWhich Hogwarts House Do You Truly Belong In?Toxic Family Test
Quizzes & Games
Pizza CalculatorAdvanced Roulette GamePlayWhat Is My Face Shape QuizTake QuizDo I Have Common Sense QuizTake QuizWhat Age Is My Brain QuizTake QuizDo You Have What It Takes To Become A Millionaire?Take Quiz
Categories
Education and Communications
Studying
Mathematics
Trigonometry
wikiHow Newsletter You're all set! Helpful how-tos delivered toyour inbox every week! Sign me up! By signing up you are agreeing to receive emails according to our privacy policy.
Home
About wikiHow
Experts
Jobs
Contact Us
Site Map
Terms of Use
Privacy Policy
Do Not Sell or Share My Info
Not Selling Info
Contribute
Follow Us
×
wikiHow Tech Help Pro:
Develop the tech skills you need for work and life
Download Article Explore this Article Steps Steps Other Sections Questions & Answers VideoWATCH NOW Related Articles Expert Interview References Article Summary Co-authored by Joseph Quinones 
2 Easy Ways to Use a Protractor 
Advertisement 
Co-authored by: Joseph Quinones Physics Teacher This article was co-authored by Joseph Quinones. Joseph Quinones is a Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. This article has been viewed 1,152,359 times. 29 votes - 82% Co-authors: 18 Updated: October 9, 2024 Views: 1,152,359 Categories: Trigonometry Article SummaryX
Take Quiz
Take Quiz
Take Quiz
Take Quiz
Take Quiz
Take Quiz 
Play
Take Quiz
Take Quiz
Take Quiz 
509 
Convert Degrees to Radians Practice Problems 
Convert Degrees to Radians Practice Problems ANSWER KEY 
1 Write down the number of degrees you want to convert to radians.[2] Let's work with a few examples so you really get the concept down. Here are the examples you'll be working with: 
2 Multiply the number of degrees by π/180.[3] To understand why you have to do this, you should know that 180 degrees constitute π radians. Therefore, 1 degree is equivalent to (π/180) radians. Since you know this, all you have to do is multiply the number of degrees you're working with by π/180 to convert it to radian terms. You can remove the degree sign since your answer will be in radians anyway. Here's how to set it up:[4] 
3 Do the math. Simply carry out the multiplication process, by multiplying the number of degrees by π/180. Think of it like multiplying two fractions: the first fraction has the number of degrees in the numerator and "1" in the denominator, and the second fraction has π in the numerator and 180 in the denominator. Here's how you do the math:[5] 
4 Simplify. Now, you've got to put each fraction in lowest terms to get your final answer. Find the largest number that can evenly divide into the numerator and denominator of each fraction and use it to simplify each fraction. The largest number for the first example is 60; for the second, it's 30, and for the third, it's 45. But you don't have to know that right away; you can just experiment by first trying to divide the numerator and denominator by 5, 2, 3, or whatever works. Here's how you do it:[6] 
5 Write down your answer. To be clear, you can write down what your original angle measure became when converted to radians. Then, you're all done! Here's what you do:[7] 
Anan Shah Community Answer Simply: π=180 or π=180*1 degree and therefore, 1degree= π/180, thus, degree measure= radian measure * π/180. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 64 Helpful 73 
Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy.