How to convert radians to degrees

To measure an angle, there are two different measuring systems. The two units used to measure an angle are radians and degrees. The unit radians is used mostly in the concept of trigonometry. The measure of angles can be converted from radians to degrees using a formula. To understand this formula and conversion of radians to degrees, we will understand the meaning of each unit of angle. We will also see the conversion table for radians to degrees in this article.

Radians to Degrees Conversion

There are two different units used to measure an angle: radians and degrees. Hence, it is important for us to be proficient in the conversion of units of angle, that is radians to degrees and degrees to radians. When we take the radius of a circle and revolve it, we start constructing an angle that can be measured in radians or degrees. Let us see what each unit of angle means and how to measure the angle.

Radians

When we rotate the radius completely around the circle, it completes one rotation. The angle subtended at the center of the circle by the radius after one complete rotation is 2π radians. The angle in radians subtended by the radius at the center of the circle is the ratio of the length of the arc to the length of the radius. When the length of the arc becomes equal to the length of the radius, the angle subtended at the center becomes 1 radian. We denote the unit radian as rad. Radians is the SI unit of measuring angles.

Degrees

Angles are measured in degrees. One revolution is divided into 360 equal parts and each part is called a degree. The angle subtended at the center of the circle after one complete rotation of the radius is 360°. The symbol for degrees is denoted by '°'. Degrees is not an SI unit to measure angles but it is an accepted unit to measure. Hence, while solving problems, it is preferred to convert the unit of angle from radians to degrees to understand it better. The instrument used to measure an angle in degrees is a protractor.
Comparing the measures of the angle for a complete rotation, we observe,
  • 360 Degrees = 2π Radians
  • 180 Degrees = π Radians

Radians to Degrees Formula

The radians to degrees formula is used to convert radians to degrees. To convert radians to degrees we need to multiply the radians by 180°/π radians. When we measure angles we use two types of units: degrees and radians, 1 degree is written as 1°. And 1 radian is written as 1 (or) 1c i.e. if there is no unit after the measure of an angle, it means that it is in radians. One rotation in a circle is divided into 360 equal parts and each part is called a degree. One complete counterclockwise rotation in radians is 2π and in degrees, it is 360°. Thus, degree measure and radian measure are related. The formula to convert an angle in radians to degrees is:
Angle in Radians × 180°/π = Angle in Degrees

One degree is equal 0.01745329252 radians:

1° = π/180° = 0.005555556π = 0.01745329252 rad

One radian is equal 57.295779513 degrees:

1 rad = 180°/π = 57.295779513°

The angle α in degrees is equal to the angle α in radians times 180 degrees divided by pi constant:

α(degrees) = α(radians) × 180° / π

or

degrees = radians × 180° / π

Example

Convert 0.5236 rad angle to degrees:

α(degrees) = α(radians) × 180° / π = 0.5236 rad × 180° / 3.1459 = 30°

How to convert degrees to radians »


Currently, we have around 5663 calculators, conversion tables and usefull online tools and software features for students, teaching and teachers, designers and simply for everyone.

You can find at this page financial calculators, mortgage calculators, calculators for loans, calculators for auto loan and lease calculators, interest calculators, payment calculators, retirement calculators, amortization calculators, investment calculators, inflation calculators, finance calculators, income tax calculators, compound interest calculators, salary calculator, interest rate calculator, sales tax calculator, fitness & health calculators, bmi calculator, calorie calculators, body fat calculator, bmr calculator, ideal weight calculator, pace calculator, pregnancy calculator, pregnancy conception calculator, due date calculator, math calculators, scientific calculator, fraction calculator, percentage calculators, random number generator, triangle calculator, standard deviation calculator, other calculators, age calculator, date calculator, time calculator, hours calculator, gpa calculator, grade calculator, concrete calculator, subnet calculator, password generator conversion calculator and many other tools and for text editing and formating, downloading videos from Facebok (we built one of the most famous Facebook video downloader online tools). We also provide you online downloanders for YouTube, Linkedin, Instagram, Twitter, Snapchat, TikTok and other social media sites (please note we does not host any videos on its servers. All videos that you download are downloaded from Facebook's, YouTube's, Linkedin's, Instagram's, Twitter's, Snapchat's, TikTok's CDNs. We also specialise on keyboard shortcuts, ALT codes for Mac, Windows and Linux and other usefull hints and tools (how to write emoji online etc.)

There are many very usefull online free tools and we would be happy if you share our page to others or send us any suggestions for other tools which will come on your mind. Also in case you find any of our tools that it does not work properly or need a better translation - please let us know. Our tools will make your life easier or simply help you to do your work or duties faster and in more effective way.

These below are the most commonly used by many users all over the world.

And we are still developing more. Our goal is to become the one-stop, go-to site for people who need to make quick calculations or who need to find quick answer for basic conversions.

Additionally, we believe the internet should be a source of free information. Therefore, all of our tools and services are completely free, with no registration required. We coded and developed each calculator individually and put each one through strict, comprehensive testing. However, please inform us if you notice even the slightest error – your input is extremely valuable to us. While most calculators on Justfreetools.com are designed to be universally applicable for worldwide usage, some are for specific countries only.


Page Id: 1018

This website uses cookies to improve your experience, analyze traffic and display ads. Learn more