Home » Radians to Degrees

Radians to Degrees


Welcome to radians to degrees, our article about the conversion of angular measures.

Skip intro and head directly to the result.


The radian measure is particularly useful in trigonometric functions and their differentiation and integration (calculus); e.g. the sine function.

The term radian means the unit circle, as detailed further below in this article on the measurement of angles.

The unit symbol for radians is rad, and degrees are often abbreviated as deg. So, if you have been looking for rad to deg, then you have also found the right page,too.

The same applies if you had entered radians to ° in your favorite search engine, because ° is the degree symbol which denotes the angle measure that divides a circle into 360 parts.

Besides decimals, our app right below also accepts the pi representations “π”,”Π”,”pi”,”Pi” and “PI” for both, angles in degrees as well as in angles in radian measure!

Radians to Degrees Calculator

Reset
Simply the Best Angle Converter Radians ⇄ Degrees! Click To TweetYou may use either field to input a value. If you edit the lower field you are changing degrees to radians. Give it a try, now!

How to Convert Radians to Degrees

Radians are SI derived and the standard unit, whereas degrees are non-SI, yet accepted by the organization International System of Units (SI).

Keep reading to learn everything about rad to degrees, and make sure to check out our converter above.

Definition: Radians are defined as circular arc / radius of the arc, so if s stands for the arc’s length, and if r denotes the radius, the angle theta (θ) is the subtended angle in the unit radian: s / r = θ, or s = rθ.

As you can see, this ratio of the two lengths s and r does not naturally have a unit symbol as it is a pure number and as such as dimensionless quantity.

Therefore, in radian measure the unit symbol rad is usually omitted. For a circular arc taking on the form of a complete circle rθ = 2πr (the circumference of a circle).

It follows that θ = 2π, which answers the question how many rad in a circle.

In turn, as detailed on our home page, the answer to how many degrees in a circle is 360.

In other words, a complete revolution is 2π, equivalent to the magnitude of 360 degrees.

Now that we know the relation between degree and radian, here’s how to obtain rad in deg: Divide the angle in radian by pi, and multiply the term by 180°.

For example, to change π/4 to degrees calculate 0.25 π / π × 180° = 0.25 × 180° = 45°. The formula can be found in the section ahead.

BTW: Positive angles show a counterclockwise revolution.

It is recommended that you make use of our calculator for any radians to degrees conversion.

Formula

Taking into account the equivalence of 2π and 360°, we can produce the radians to degrees formula, also known as radians to degrees equation:



The formula is to be used as this: simply substitute rad with your angle in radian and do the math.
  • Example 1: π/2 → 90°
  • Example 2: π/3 → 60°
  • Example 3: π/4 → 45°
If you want it even easier make use of our app or consult the table below.

To use our converter insert the magnitude of your angle in radians, our tool then does the rest automatically for you, including rounding the result to nine decimal places.

Calculator

To improve user experience we have moved our converter to the top of this page.

If you press “reset”, then our app reinitializes the conversion, but if you fill in the lower field our tool inverts the calculation to degrees to radians.

More calculators like the one under consideration can be found following the links useful sites, located in the sidebar of the home page.

Our frequent conversions include: BTW: If you come across the terms degree of arc, arc degree, or arcdegree, this is the full spelling for the unit of measurement of an angle, to differentiate it from temperature (degrees).

Ahead is the explanation of the form search conversions which can be used to convert angles, because many values have already been converted by us.

Rad to Deg Table

The table below contains frequent angles:
RadiansDegrees
0 rad
π/12 ≈ 0.261799388 rad15°
π/6 ≈ 0.523598776 rad30°
π/4 ≈ 0.785398163 rad45°
π/3 ≈ 1.047197551 rad60°
5π/12 ≈ 1.308996939 rad75°
π/2 ≈ 1.570796327 rad90°
7π/12 ≈ 1.832595715 rad105°
2π/3 ≈ 2.094395102 rad120°
3π/4 ≈ 2.35619449 rad135°
5π/6 ≈ 2.617993878 rad150°
11π/12 ≈ 2.879793266 rad165°
π ≈ 3.141592654 rad180°
13π/12 ≈ 3.403392041 rad195°
7π/6 ≈ 3.665191429 rad210°
5π/4 ≈ 3.926990817 rad225°
4π/3 ≈ 4.188790205 rad240°
17π/12 ≈ 4.450589593 rad255°
3π/2 ≈ 4.71238898 rad270°
19π/12 ≈ 4.974188368 rad285°
5π/3 ≈ 5.235987756 rad300°
7π/4 ≈ 5.497787144 rad315°
11π/6 ≈ 5.759586532 rad330°
23π/12 ≈ 6.021385919 rad345°
2π ≈ 6.283185307 rad360°

Converting Rad to Deg

In case you are primarily interested in the result, and making use of our angle conversion tool is inconvenient, such as, for example, whist using a mobile phone, you can utilize our search form.

Simply insert your query in the aforementioned form, and you will be redirect to a result page, which displays the closest match for your particular query.

The results most likely include the conversion you have been looking for.

The form is displayed to you in the sidebar for desktop and tablet computer visitors, as well as in our menu.

Users having a mobile device need to scroll down towards the end of this page or click on the search menu item. To use the form type x rad to °, provided that x is you angle.

Here you can change degrees to radians.

In the following paragraph we will review the FAQs in the context of this article.

Frequently Asked Questions

Click on the question which is of interest to you to see the collapsible content answer.

How do you convert from radians to degrees?

Multiply by the value in radians by 180/pi to get degrees.

What is meant by 1 radian?

1 radian is approximately 57.295779513 degrees.

Is pi equal to 180 degrees?

The perimeter of a circle is 360 degrees = 2 pi radian. So, for 180 degrees the 1/2 circle is equivalent to pi.

How many radians in a circle?

In every circle there are 2 pi radians.

Why is PI 180 degrees?

As the circumference of 360 degrees is equivalent to 2 PI, PI = 180 degrees.

How to turn radians into degrees?

To obtain degrees, divide the angle in radian by pi, then multiply the term by 180 degrees.

How many radians is degrees in pi?

One complete revolution (360°) = 2pi. Thus, pi equals 180°.
If you have been reading our information from the beginning, then coming up with the answers should be easy for you.

However, if something remains unclear just get in touch with us.

Make sure to understand that it is the unit radian, not degrees, that makes math easier.

This may seem counter-intuitive, but that’s why in trigonometry the arguments are often stated in rad.

Degrees indicate how far we tilt our heads to conceive angles and rotations, whereas rad, which can be thought of as radius units, are about the distance on an arc traveled.

This essentially means that the unit degree is from the perspective of an observer (an arc), in contrast to unit radian which reflects the viewpoint of a mover (a straight line).

Next you can find the conversion of frequent angles, followed by the summary of our content.

Conclusion

You have reached the end of our information regarding the unit conversion of plane angles, which we summarize using this image:

An angle’s magnitude in radians is mostly expressed in radian measurement, such as in the cosine function for example.

Visitors who have been searching for radian definition, or a similar term should also have found theirs answers.

The simple formula is that 2pi radians equal 360 degrees, which means that π radians equal 180 degrees.

Here are the equivalences of some common angles:
  • π/12 ⇔ 15°
  • π/6 ⇔ 30°
  • π/5 ⇔ 36°
  • π/4 ⇔ 45°
  • π/3 ⇔ 60°
  • 2π/5 ⇔ 72°
  • π/2 ⇔ 90°
  • 2π/3 ⇔ 120°
  • 4π/5 ⇔ 144°
  • π ⇔ 180°
  • 3π/2 ⇔ 270°
  • 2π ⇔ 360°

Additional Information on Rad to Deg

Keep in mind that anticlockwise revolution means an angle is positive.

For feedback, including all questions and comments, use the designated form at the bottom of this page.

Alternatively, you may send us an email with a clear subject line.

If our information on radians and degrees and the converter have been useful to you, please hit the social buttons to let everybody know about our website, and don’t forget to bookmark us.

For further information on radian to degrees check out the sites listed on our homepage.

Thanks for your visit.