How to Convert Radians to 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.

In any case it is recommended that you also check out our converter further below.

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:
$deg \hspace{5px}=\hspace{5px} \frac{rad}{\pi} \times\hspace{5px} 180^{\circ}\hspace{45px}$

The formula is to be used as this: simply substitute rad with your angle in radian and do the math. If you want it even easier make use of our calculator in the next paragraph.

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

Calculator

°:

Don’t press the button unless you want to swap the units. More calculators like this 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.

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.

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 radians to °, provided that x is you angle in rad.

Here you can change degrees to radians.

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

• How to convert from radians to degrees?
• How many radians in a circle?
• How to convert radians into degrees?
• How to change radians to degrees?
• How to convert radian to degree?

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 radians.

Degrees indicate how far we tilt our heads to conceive angles and rotations, whereas radians, 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:

Visitors who have been searching for how many radians in a circle, radian definition, or a similar term should also have found theirs answers.

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°

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